All the Solutions to Hofsdater's Q-recurrence with initial 2 initial conditi\ ons between 1 and, 10 That happen to have Rational Generating Functions By Shalosh B. Ekhad Recall that the famous (or, more accurately, infamous), Hofsdater's Q-sequen\ ce, Sequence A005185 in the OEIS is defined by the intial conditions Q(1)=1, Q(2)=1, and for n>2 by Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2)) It seems to be completely "chaotic". Nevertheless, if instead of the initial\ conditions [1,1], one takes the following one, one gets sequences whose generating functions are rational. 17 14 13 12 11 INI= , [1, 1, 3], Generating Function=, (-t - 4 t + t - t - 3 t 10 9 8 7 6 4 3 2 / 9 3 - 2 t - t + t - 5 t - t + 2 t + 3 t + t + t) / (t - 2 t + 1) / and in Maple notation: (-t^17-4*t^14+t^13-t^12-3*t^11-2*t^10-t^9+t^8-5*t^7-t^6+2*t^4+3*t^3+t^2+t)/(t^9 -2*t^3+1) 6 5 4 3 2 t - 3 t + 2 t + 2 t + 3 t + t INI= , [1, 3, 2], Generating Function=, ---------------------------------- 6 3 t - 2 t + 1 and in Maple notation: (t^6-3*t^5+2*t^4+2*t^3+3*t^2+t)/(t^6-2*t^3+1) 6 5 4 3 2 -3 t - t + t + 3 t + t + 2 t INI= , [2, 1, 3], Generating Function=, --------------------------------- 6 3 t - 2 t + 1 and in Maple notation: (-3*t^6-t^5+t^4+3*t^3+t^2+2*t)/(t^6-2*t^3+1) INI= , [2, 1, 4], Generating Function=, 9 8 7 6 5 4 2 -2 t + 2 t + 4 t - 5 t - 2 t + 2 t + t + 2 t --------------------------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (-2*t^9+2*t^8+4*t^7-5*t^6-2*t^5+2*t^4+t^2+2*t)/(t^4-2*t^2+1) 4 2 -2 t + 2 t + 2 t INI= , [2, 2, 4], Generating Function=, ------------------ 4 2 t - 2 t + 1 and in Maple notation: (-2*t^4+2*t^2+2*t)/(t^4-2*t^2+1) 7 5 4 3 2 2 t - 4 t - 2 t + 2 t + 2 t + 2 t INI= , [2, 2, 6], Generating Function=, -------------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^7-4*t^5-2*t^4+2*t^3+2*t^2+2*t)/(t^4-2*t^2+1) 9 5 4 3 2 2 t - 6 t - 2 t + 4 t + 2 t + 2 t INI= , [2, 2, 8], Generating Function=, -------------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^9-6*t^5-2*t^4+4*t^3+2*t^2+2*t)/(t^4-2*t^2+1) INI= , [2, 2, 10], Generating Function=, 11 5 4 3 2 2 t - 8 t - 2 t + 6 t + 2 t + 2 t --------------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^11-8*t^5-2*t^4+6*t^3+2*t^2+2*t)/(t^4-2*t^2+1) 7 6 4 3 2 -t - t - t + t + 3 t + 2 t INI= , [2, 3, 1], Generating Function=, ------------------------------- 6 3 t - 2 t + 1 and in Maple notation: (-t^7-t^6-t^4+t^3+3*t^2+2*t)/(t^6-2*t^3+1) 4 3 2 -t - 2 t + 3 t + 2 t INI= , [2, 3, 2], Generating Function=, ----------------------- 4 2 t - 2 t + 1 and in Maple notation: (-t^4-2*t^3+3*t^2+2*t)/(t^4-2*t^2+1) 6 4 2 t - 4 t + 3 t + 2 t INI= , [2, 3, 4], Generating Function=, ---------------------- 4 2 t - 2 t + 1 and in Maple notation: (t^6-4*t^4+3*t^2+2*t)/(t^4-2*t^2+1) INI= , [2, 3, 5], Generating Function=, 10 9 8 7 6 5 4 3 2 2 t - t - 4 t + 3 t + 3 t - 3 t - 4 t + t + 3 t + 2 t --------------------------------------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^10-t^9-4*t^8+3*t^7+3*t^6-3*t^5-4*t^4+t^3+3*t^2+2*t)/(t^4-2*t^2+1) INI= , [2, 3, 6], Generating Function=, 7 6 5 4 3 2 2 t + t - 4 t - 4 t + 2 t + 3 t + 2 t ------------------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^7+t^6-4*t^5-4*t^4+2*t^3+3*t^2+2*t)/(t^4-2*t^2+1) INI= , [2, 3, 7], Generating Function=, 12 11 10 9 8 6 5 4 3 2 2 t - t - 4 t + 3 t + 2 t + t - 5 t - 4 t + 3 t + 3 t + 2 t ------------------------------------------------------------------------ 4 2 t - 2 t + 1 and in Maple notation: (2*t^12-t^11-4*t^10+3*t^9+2*t^8+t^6-5*t^5-4*t^4+3*t^3+3*t^2+2*t)/(t^4-2*t^2+1) INI= , [2, 3, 8], Generating Function=, 9 6 5 4 3 2 2 t + t - 6 t - 4 t + 4 t + 3 t + 2 t ------------------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^9+t^6-6*t^5-4*t^4+4*t^3+3*t^2+2*t)/(t^4-2*t^2+1) INI= , [2, 3, 9], Generating Function=, ( 14 13 12 11 10 6 5 4 3 2 2 t - t - 4 t + 3 t + 2 t + t - 7 t - 4 t + 5 t + 3 t + 2 t) / 4 2 / (t - 2 t + 1) / and in Maple notation: (2*t^14-t^13-4*t^12+3*t^11+2*t^10+t^6-7*t^5-4*t^4+5*t^3+3*t^2+2*t)/(t^4-2*t^2+1 ) INI= , [2, 3, 10], Generating Function=, 11 6 5 4 3 2 2 t + t - 8 t - 4 t + 6 t + 3 t + 2 t -------------------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^11+t^6-8*t^5-4*t^4+6*t^3+3*t^2+2*t)/(t^4-2*t^2+1) 7 2 -2 t + 4 t + 2 t INI= , [2, 4, 2], Generating Function=, ------------------ 6 4 2 t - t - t + 1 and in Maple notation: (-2*t^7+4*t^2+2*t)/(t^6-t^4-t^2+1) INI= , [2, 4, 3], Generating Function=, 10 8 7 6 5 4 3 2 -2 t + 4 t - t - 4 t + 2 t - 2 t + t + 4 t + 2 t --------------------------------------------------------- 6 4 2 t - t - t + 1 and in Maple notation: (-2*t^10+4*t^8-t^7-4*t^6+2*t^5-2*t^4+t^3+4*t^2+2*t)/(t^6-t^4-t^2+1) 6 4 3 2 2 t - 5 t - 2 t + 5 t + 2 t INI= , [2, 5, 2], Generating Function=, ------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^6-5*t^4-2*t^3+5*t^2+2*t)/(t^4-2*t^2+1) INI= , [2, 5, 3], Generating Function=, 9 7 6 5 4 3 2 2 t - 5 t + 3 t + 4 t - 8 t - t + 5 t + 2 t -------------------------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^9-5*t^7+3*t^6+4*t^5-8*t^4-t^3+5*t^2+2*t)/(t^4-2*t^2+1) 9 2 -2 t + 6 t + 2 t INI= , [2, 6, 2], Generating Function=, ------------------ 8 6 2 t - t - t + 1 and in Maple notation: (-2*t^9+6*t^2+2*t)/(t^8-t^6-t^2+1) INI= , [2, 6, 3], Generating Function=, 12 10 9 8 7 5 4 3 2 -2 t + 6 t - t - 6 t - 2 t + 6 t - 4 t + t + 6 t + 2 t ----------------------------------------------------------------- 8 6 2 t - t - t + 1 and in Maple notation: (-2*t^12+6*t^10-t^9-6*t^8-2*t^7+6*t^5-4*t^4+t^3+6*t^2+2*t)/(t^8-t^6-t^2+1) 8 4 3 2 2 t - 7 t - 2 t + 7 t + 2 t INI= , [2, 7, 2], Generating Function=, ------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^8-7*t^4-2*t^3+7*t^2+2*t)/(t^4-2*t^2+1) INI= , [2, 7, 3], Generating Function=, 11 7 6 5 4 3 2 2 t - 7 t + 5 t + 6 t - 12 t - t + 7 t + 2 t ---------------------------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^11-7*t^7+5*t^6+6*t^5-12*t^4-t^3+7*t^2+2*t)/(t^4-2*t^2+1) 11 2 -2 t + 8 t + 2 t INI= , [2, 8, 2], Generating Function=, ------------------- 10 8 2 t - t - t + 1 and in Maple notation: (-2*t^11+8*t^2+2*t)/(t^10-t^8-t^2+1) INI= , [2, 8, 3], Generating Function=, 14 12 11 10 9 5 4 3 2 -2 t + 8 t - t - 8 t - 2 t + 8 t - 6 t + t + 8 t + 2 t ------------------------------------------------------------------- 10 8 2 t - t - t + 1 and in Maple notation: (-2*t^14+8*t^12-t^11-8*t^10-2*t^9+8*t^5-6*t^4+t^3+8*t^2+2*t)/(t^10-t^8-t^2+1) 10 4 3 2 2 t - 9 t - 2 t + 9 t + 2 t INI= , [2, 9, 2], Generating Function=, -------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^10-9*t^4-2*t^3+9*t^2+2*t)/(t^4-2*t^2+1) INI= , [2, 9, 3], Generating Function=, 13 7 6 5 4 3 2 2 t - 9 t + 7 t + 8 t - 16 t - t + 9 t + 2 t ---------------------------------------------------- 4 2 t - 2 t + 1 and in Maple notation: (2*t^13-9*t^7+7*t^6+8*t^5-16*t^4-t^3+9*t^2+2*t)/(t^4-2*t^2+1) 13 2 -2 t + 10 t + 2 t INI= , [2, 10, 2], Generating Function=, -------------------- 12 10 2 t - t - t + 1 and in Maple notation: (-2*t^13+10*t^2+2*t)/(t^12-t^10-t^2+1) INI= , [2, 10, 3], Generating Function=, 16 14 13 12 11 5 4 3 2 -2 t + 10 t - t - 10 t - 2 t + 10 t - 8 t + t + 10 t + 2 t ------------------------------------------------------------------------ 12 10 2 t - t - t + 1 and in Maple notation: (-2*t^16+10*t^14-t^13-10*t^12-2*t^11+10*t^5-8*t^4+t^3+10*t^2+2*t)/(t^12-t^10-t^ 2+1) 6 5 4 3 2 2 t + t - 3 t + t + 2 t + 3 t INI= , [3, 2, 1], Generating Function=, ---------------------------------- 6 3 t - 2 t + 1 and in Maple notation: (2*t^6+t^5-3*t^4+t^3+2*t^2+3*t)/(t^6-2*t^3+1) 6 5 4 3 2 -6 t - 6 t - 3 t + 3 t + 3 t + 3 t INI= , [3, 3, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-6*t^5-3*t^4+3*t^3+3*t^2+3*t)/(2*t^6-3*t^3+1) 6 5 4 3 2 -5 t - 6 t - 6 t + 5 t + 3 t + 3 t INI= , [3, 3, 5], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-5*t^6-6*t^5-6*t^4+5*t^3+3*t^2+3*t)/(2*t^6-3*t^3+1) 6 5 4 3 2 -6 t - 6 t - 6 t + 6 t + 3 t + 3 t INI= , [3, 3, 6], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-6*t^5-6*t^4+6*t^3+3*t^2+3*t)/(2*t^6-3*t^3+1) 6 5 4 3 2 -7 t - 6 t - 6 t + 7 t + 3 t + 3 t INI= , [3, 3, 7], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-7*t^6-6*t^5-6*t^4+7*t^3+3*t^2+3*t)/(2*t^6-3*t^3+1) 6 5 4 3 2 -8 t - 6 t - 6 t + 8 t + 3 t + 3 t INI= , [3, 3, 8], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-8*t^6-6*t^5-6*t^4+8*t^3+3*t^2+3*t)/(2*t^6-3*t^3+1) 6 5 4 3 2 -9 t - 6 t - 6 t + 9 t + 3 t + 3 t INI= , [3, 3, 9], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-9*t^6-6*t^5-6*t^4+9*t^3+3*t^2+3*t)/(2*t^6-3*t^3+1) INI= , [3, 3, 10], Generating Function=, 6 5 4 3 2 -10 t - 6 t - 6 t + 10 t + 3 t + 3 t ----------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-10*t^6-6*t^5-6*t^4+10*t^3+3*t^2+3*t)/(2*t^6-3*t^3+1) 6 5 4 3 2 -6 t - 4 t - 6 t + 3 t + 4 t + 3 t INI= , [3, 4, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-4*t^5-6*t^4+3*t^3+4*t^2+3*t)/(2*t^6-3*t^3+1) 13 12 10 9 8 INI= , [3, 5, 2], Generating Function=, (-t + 3 t + 3 t - 5 t + 4 t 7 6 5 4 3 2 / 10 5 - 8 t + 2 t + 2 t + 5 t + 2 t + 5 t + 3 t) / (t - 2 t + 1) / and in Maple notation: (-t^13+3*t^12+3*t^10-5*t^9+4*t^8-8*t^7+2*t^6+2*t^5+5*t^4+2*t^3+5*t^2+3*t)/(t^10 -2*t^5+1) 6 5 4 3 2 -6 t - 5 t - 6 t + 3 t + 5 t + 3 t INI= , [3, 5, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-5*t^5-6*t^4+3*t^3+5*t^2+3*t)/(2*t^6-3*t^3+1) 6 5 4 3 2 -6 t - 6 t - 6 t + 3 t + 6 t + 3 t INI= , [3, 6, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-6*t^5-6*t^4+3*t^3+6*t^2+3*t)/(2*t^6-3*t^3+1) 6 5 4 3 2 -6 t - 7 t - 6 t + 3 t + 7 t + 3 t INI= , [3, 7, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-7*t^5-6*t^4+3*t^3+7*t^2+3*t)/(2*t^6-3*t^3+1) 6 5 4 3 2 -6 t - 8 t - 6 t + 3 t + 8 t + 3 t INI= , [3, 8, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-8*t^5-6*t^4+3*t^3+8*t^2+3*t)/(2*t^6-3*t^3+1) 6 5 4 3 2 -6 t - 9 t - 6 t + 3 t + 9 t + 3 t INI= , [3, 9, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-9*t^5-6*t^4+3*t^3+9*t^2+3*t)/(2*t^6-3*t^3+1) INI= , [3, 10, 3], Generating Function=, 6 5 4 3 2 -6 t - 10 t - 6 t + 3 t + 10 t + 3 t ----------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-10*t^5-6*t^4+3*t^3+10*t^2+3*t)/(2*t^6-3*t^3+1) INI= , [4, 2, 2], Generating Function=, 10 9 8 7 6 4 3 2 2 t - 4 t - 2 t + 6 t - 4 t + 2 t - 2 t + 2 t + 4 t ------------------------------------------------------------ 6 4 2 t - t - t + 1 and in Maple notation: (2*t^10-4*t^9-2*t^8+6*t^7-4*t^6+2*t^4-2*t^3+2*t^2+4*t)/(t^6-t^4-t^2+1) 6 2 -2 t + 2 t + 4 t INI= , [4, 2, 4], Generating Function=, ------------------ 6 4 2 t - t - t + 1 and in Maple notation: (-2*t^6+2*t^2+4*t)/(t^6-t^4-t^2+1) 7 6 5 3 2 2 t - 2 t - 4 t + 2 t + 2 t + 4 t INI= , [4, 2, 6], Generating Function=, -------------------------------------- 6 4 2 t - t - t + 1 and in Maple notation: (2*t^7-2*t^6-4*t^5+2*t^3+2*t^2+4*t)/(t^6-t^4-t^2+1) INI= , [4, 2, 8], Generating Function=, 9 7 6 5 3 2 4 t - 4 t - 2 t - 4 t + 4 t + 2 t + 4 t --------------------------------------------- 6 4 2 t - t - t + 1 and in Maple notation: (4*t^9-4*t^7-2*t^6-4*t^5+4*t^3+2*t^2+4*t)/(t^6-t^4-t^2+1) INI= , [4, 2, 10], Generating Function=, 11 7 6 5 3 2 4 t - 6 t - 2 t - 4 t + 6 t + 2 t + 4 t ---------------------------------------------- 6 4 2 t - t - t + 1 and in Maple notation: (4*t^11-6*t^7-2*t^6-4*t^5+6*t^3+2*t^2+4*t)/(t^6-t^4-t^2+1) INI= , [4, 3, 2], Generating Function=, 7 6 5 4 3 2 2 t - 3 t - 4 t + 4 t - 2 t + 3 t + 4 t --------------------------------------------- 6 4 2 t - t - t + 1 and in Maple notation: (2*t^7-3*t^6-4*t^5+4*t^4-2*t^3+3*t^2+4*t)/(t^6-t^4-t^2+1) 6 5 4 3 2 -6 t - 6 t - 4 t + 3 t + 3 t + 4 t INI= , [4, 3, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-6*t^5-4*t^4+3*t^3+3*t^2+4*t)/(2*t^6-3*t^3+1) 20 19 18 17 16 INI= , [4, 3, 5], Generating Function=, (t - 6 t - 3 t + 5 t - 6 t 15 14 13 12 11 10 9 8 7 - 4 t - 4 t + 9 t - 3 t - 4 t + 13 t + 6 t + 3 t + 9 t 6 5 4 3 2 / 20 10 + 6 t + 4 t + 4 t + 5 t + 3 t + 4 t) / (t - 2 t + 1) / and in Maple notation: (t^20-6*t^19-3*t^18+5*t^17-6*t^16-4*t^15-4*t^14+9*t^13-3*t^12-4*t^11+13*t^10+6* t^9+3*t^8+9*t^7+6*t^6+4*t^5+4*t^4+5*t^3+3*t^2+4*t)/(t^20-2*t^10+1) 19 18 17 16 15 INI= , [4, 3, 6], Generating Function=, (-6 t - 3 t + 4 t - 6 t - 4 t 14 13 12 11 10 9 8 7 6 - 4 t + 8 t - 3 t - 4 t + 14 t + 6 t + 3 t + 10 t + 6 t 5 4 3 2 / 20 10 + 4 t + 4 t + 6 t + 3 t + 4 t) / (t - 2 t + 1) / and in Maple notation: (-6*t^19-3*t^18+4*t^17-6*t^16-4*t^15-4*t^14+8*t^13-3*t^12-4*t^11+14*t^10+6*t^9+ 3*t^8+10*t^7+6*t^6+4*t^5+4*t^4+6*t^3+3*t^2+4*t)/(t^20-2*t^10+1) 20 19 18 17 16 INI= , [4, 3, 7], Generating Function=, (-t - 6 t - 3 t + 3 t - 6 t 15 14 13 12 11 10 9 8 7 - 4 t - 4 t + 7 t - 3 t - 4 t + 15 t + 6 t + 3 t + 11 t 6 5 4 3 2 / 20 10 + 6 t + 4 t + 4 t + 7 t + 3 t + 4 t) / (t - 2 t + 1) / and in Maple notation: (-t^20-6*t^19-3*t^18+3*t^17-6*t^16-4*t^15-4*t^14+7*t^13-3*t^12-4*t^11+15*t^10+6 *t^9+3*t^8+11*t^7+6*t^6+4*t^5+4*t^4+7*t^3+3*t^2+4*t)/(t^20-2*t^10+1) 20 19 18 17 16 INI= , [4, 3, 8], Generating Function=, (-2 t - 6 t - 3 t + 2 t - 6 t 15 14 13 12 11 10 9 8 7 - 4 t - 4 t + 6 t - 3 t - 4 t + 16 t + 6 t + 3 t + 12 t 6 5 4 3 2 / 20 10 + 6 t + 4 t + 4 t + 8 t + 3 t + 4 t) / (t - 2 t + 1) / and in Maple notation: (-2*t^20-6*t^19-3*t^18+2*t^17-6*t^16-4*t^15-4*t^14+6*t^13-3*t^12-4*t^11+16*t^10 +6*t^9+3*t^8+12*t^7+6*t^6+4*t^5+4*t^4+8*t^3+3*t^2+4*t)/(t^20-2*t^10+1) 20 19 18 17 16 INI= , [4, 3, 9], Generating Function=, (-3 t - 6 t - 3 t + t - 6 t 15 14 13 12 11 10 9 8 7 - 4 t - 4 t + 5 t - 3 t - 4 t + 17 t + 6 t + 3 t + 13 t 6 5 4 3 2 / 20 10 + 6 t + 4 t + 4 t + 9 t + 3 t + 4 t) / (t - 2 t + 1) / and in Maple notation: (-3*t^20-6*t^19-3*t^18+t^17-6*t^16-4*t^15-4*t^14+5*t^13-3*t^12-4*t^11+17*t^10+6 *t^9+3*t^8+13*t^7+6*t^6+4*t^5+4*t^4+9*t^3+3*t^2+4*t)/(t^20-2*t^10+1) 20 19 18 16 INI= , [4, 3, 10], Generating Function=, (-4 t - 6 t - 3 t - 6 t 15 14 13 12 11 10 9 8 7 - 4 t - 4 t + 4 t - 3 t - 4 t + 18 t + 6 t + 3 t + 14 t 6 5 4 3 2 / 20 10 + 6 t + 4 t + 4 t + 10 t + 3 t + 4 t) / (t - 2 t + 1) / and in Maple notation: (-4*t^20-6*t^19-3*t^18-6*t^16-4*t^15-4*t^14+4*t^13-3*t^12-4*t^11+18*t^10+6*t^9+ 3*t^8+14*t^7+6*t^6+4*t^5+4*t^4+10*t^3+3*t^2+4*t)/(t^20-2*t^10+1) 25 24 22 21 20 INI= , [4, 4, 3], Generating Function=, (2 t - 2 t + 2 t - 2 t - 4 t 19 18 17 16 15 14 13 12 11 - 4 t + 2 t - 3 t - 4 t + 4 t - 2 t - 3 t + 8 t - 2 t 10 9 8 7 6 5 4 3 2 + 4 t + 4 t + 12 t + 3 t + 4 t + 8 t + 4 t + 3 t + 4 t + 4 t) / 20 10 / (t - 2 t + 1) / and in Maple notation: (2*t^25-2*t^24+2*t^22-2*t^21-4*t^20-4*t^19+2*t^18-3*t^17-4*t^16+4*t^15-2*t^14-3 *t^13+8*t^12-2*t^11+4*t^10+4*t^9+12*t^8+3*t^7+4*t^6+8*t^5+4*t^4+3*t^3+4*t^2+4*t )/(t^20-2*t^10+1) 7 6 5 3 2 2 t - t - 4 t - 2 t + 5 t + 4 t INI= , [4, 5, 2], Generating Function=, ------------------------------------ 6 4 2 t - t - t + 1 and in Maple notation: (2*t^7-t^6-4*t^5-2*t^3+5*t^2+4*t)/(t^6-t^4-t^2+1) 9 3 2 -2 t - 2 t + 6 t + 4 t INI= , [4, 6, 2], Generating Function=, ------------------------- 8 6 2 t - t - t + 1 and in Maple notation: (-2*t^9-2*t^3+6*t^2+4*t)/(t^8-t^6-t^2+1) INI= , [4, 7, 2], Generating Function=, 8 7 6 5 3 2 4 t + 2 t - 7 t - 4 t - 2 t + 7 t + 4 t --------------------------------------------- 6 4 2 t - t - t + 1 and in Maple notation: (4*t^8+2*t^7-7*t^6-4*t^5-2*t^3+7*t^2+4*t)/(t^6-t^4-t^2+1) 11 3 2 -2 t - 2 t + 8 t + 4 t INI= , [4, 8, 2], Generating Function=, -------------------------- 10 8 2 t - t - t + 1 and in Maple notation: (-2*t^11-2*t^3+8*t^2+4*t)/(t^10-t^8-t^2+1) INI= , [4, 9, 2], Generating Function=, 10 7 6 5 3 2 4 t + 2 t - 9 t - 4 t - 2 t + 9 t + 4 t ---------------------------------------------- 6 4 2 t - t - t + 1 and in Maple notation: (4*t^10+2*t^7-9*t^6-4*t^5-2*t^3+9*t^2+4*t)/(t^6-t^4-t^2+1) 13 3 2 -2 t - 2 t + 10 t + 4 t INI= , [4, 10, 2], Generating Function=, --------------------------- 12 10 2 t - t - t + 1 and in Maple notation: (-2*t^13-2*t^3+10*t^2+4*t)/(t^12-t^10-t^2+1) 6 5 4 3 2 -6 t - 6 t - 5 t + 3 t + 3 t + 5 t INI= , [5, 3, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-6*t^5-5*t^4+3*t^3+3*t^2+5*t)/(2*t^6-3*t^3+1) 19 18 17 16 14 INI= , [5, 7, 2], Generating Function=, (-3 t + 5 t - 3 t + 5 t + 5 t 13 12 11 10 9 8 7 6 5 - 7 t + 8 t - 12 t + 8 t - 12 t + 2 t + 2 t + 7 t + 2 t 4 3 2 / 14 7 + 7 t + 2 t + 7 t + 5 t) / (t - 2 t + 1) / and in Maple notation: (-3*t^19+5*t^18-3*t^17+5*t^16+5*t^14-7*t^13+8*t^12-12*t^11+8*t^10-12*t^9+2*t^8+ 2*t^7+7*t^6+2*t^5+7*t^4+2*t^3+7*t^2+5*t)/(t^14-2*t^7+1) 13 12 11 10 9 INI= , [6, 2, 1], Generating Function=, (3 t - 4 t - 4 t - t + 5 t 8 7 6 5 4 3 2 / + 4 t - 9 t + 4 t + 4 t + t - 5 t + 2 t + 6 t) / ( / 8 6 2 t - t - t + 1) and in Maple notation: (3*t^13-4*t^12-4*t^11-t^10+5*t^9+4*t^8-9*t^7+4*t^6+4*t^5+t^4-5*t^3+2*t^2+6*t)/( t^8-t^6-t^2+1) 12 11 10 9 8 INI= , [6, 2, 2], Generating Function=, (2 t - 6 t - 2 t + 10 t - 2 t 7 6 5 4 3 2 / 8 6 2 - 6 t - 2 t + 6 t + 2 t - 4 t + 2 t + 6 t) / (t - t - t + 1) / and in Maple notation: (2*t^12-6*t^11-2*t^10+10*t^9-2*t^8-6*t^7-2*t^6+6*t^5+2*t^4-4*t^3+2*t^2+6*t)/(t^ 8-t^6-t^2+1) 22 21 20 19 18 INI= , [6, 2, 3], Generating Function=, (9 t - 5 t - t - 6 t - 6 t 17 16 15 14 13 12 11 10 9 8 + 9 t - 5 t - t + t + 6 t + 6 t - 2 t - 10 t + 9 t - 2 t 7 5 4 3 2 / 8 6 2 - 6 t - t + 6 t - 3 t + 2 t + 6 t) / (t - t - t + 1) / and in Maple notation: (9*t^22-5*t^21-t^20-6*t^19-6*t^18+9*t^17-5*t^16-t^15+t^14+6*t^13+6*t^12-2*t^11-\ 10*t^10+9*t^9-2*t^8-6*t^7-t^5+6*t^4-3*t^3+2*t^2+6*t)/(t^8-t^6-t^2+1) INI= , [6, 2, 4], Generating Function=, 9 8 7 5 3 2 2 t - 2 t - 6 t + 6 t - 2 t + 2 t + 6 t --------------------------------------------- 8 6 2 t - t - t + 1 and in Maple notation: (2*t^9-2*t^8-6*t^7+6*t^5-2*t^3+2*t^2+6*t)/(t^8-t^6-t^2+1) 61 60 59 58 INI= , [6, 2, 5], Generating Function=, (49 t - 41 t - 25 t + 18 t 56 55 54 53 52 51 50 49 + 8 t - 54 t + 39 t + 26 t - 27 t + 3 t - 7 t - 6 t 48 47 46 45 44 43 42 41 + 34 t + 12 t - 37 t - 12 t + 43 t + 2 t - 59 t + 10 t 40 39 38 37 36 35 34 33 + 46 t - 8 t - 24 t + 6 t + 16 t - 11 t - 8 t + 6 t 32 30 29 28 27 24 23 22 21 - 2 t + 7 t - 4 t - 6 t + 6 t - 2 t - 10 t + 18 t + 5 t 20 19 18 17 15 14 13 12 11 - 13 t + 2 t - 3 t + 3 t - 6 t + t + 4 t + 3 t - t 10 9 8 7 6 3 2 / - 4 t + 7 t - 2 t - 9 t + 6 t - t + 2 t + 6 t) / ( / 8 6 2 t - t - t + 1) and in Maple notation: (49*t^61-41*t^60-25*t^59+18*t^58+8*t^56-54*t^55+39*t^54+26*t^53-27*t^52+3*t^51-\ 7*t^50-6*t^49+34*t^48+12*t^47-37*t^46-12*t^45+43*t^44+2*t^43-59*t^42+10*t^41+46 *t^40-8*t^39-24*t^38+6*t^37+16*t^36-11*t^35-8*t^34+6*t^33-2*t^32+7*t^30-4*t^29-\ 6*t^28+6*t^27-2*t^24-10*t^23+18*t^22+5*t^21-13*t^20+2*t^19-3*t^18+3*t^17-6*t^15 +t^14+4*t^13+3*t^12-t^11-4*t^10+7*t^9-2*t^8-9*t^7+6*t^6-t^3+2*t^2+6*t)/(t^8-t^6 -t^2+1) 8 2 -2 t + 2 t + 6 t INI= , [6, 2, 6], Generating Function=, ------------------ 8 6 2 t - t - t + 1 and in Maple notation: (-2*t^8+2*t^2+6*t)/(t^8-t^6-t^2+1) 28 27 26 25 24 INI= , [6, 2, 7], Generating Function=, (14 t - 18 t - t + 11 t - 6 t 23 22 21 19 18 17 16 15 14 + t - 14 t + 15 t - 4 t + 2 t - t + 4 t + 2 t - 5 t 13 12 11 10 8 7 3 2 / - 7 t + 4 t + 6 t - 4 t + 4 t - 6 t + t + 2 t + 6 t) / ( / 8 6 2 t - t - t + 1) and in Maple notation: (14*t^28-18*t^27-t^26+11*t^25-6*t^24+t^23-14*t^22+15*t^21-4*t^19+2*t^18-t^17+4* t^16+2*t^15-5*t^14-7*t^13+4*t^12+6*t^11-4*t^10+4*t^8-6*t^7+t^3+2*t^2+6*t)/(t^8- t^6-t^2+1) 9 8 7 3 2 4 t - 2 t - 6 t + 2 t + 2 t + 6 t INI= , [6, 2, 8], Generating Function=, -------------------------------------- 8 6 2 t - t - t + 1 and in Maple notation: (4*t^9-2*t^8-6*t^7+2*t^3+2*t^2+6*t)/(t^8-t^6-t^2+1) INI= , [6, 2, 10], Generating Function=, 11 9 8 7 3 2 6 t - 4 t - 2 t - 6 t + 4 t + 2 t + 6 t ---------------------------------------------- 8 6 2 t - t - t + 1 and in Maple notation: (6*t^11-4*t^9-2*t^8-6*t^7+4*t^3+2*t^2+6*t)/(t^8-t^6-t^2+1) INI= , [6, 3, 2], Generating Function=, 9 8 7 4 3 2 4 t - 3 t - 6 t + 6 t - 4 t + 3 t + 6 t --------------------------------------------- 8 6 2 t - t - t + 1 and in Maple notation: (4*t^9-3*t^8-6*t^7+6*t^4-4*t^3+3*t^2+6*t)/(t^8-t^6-t^2+1) 6 5 4 3 2 -6 t - 6 t - 6 t + 3 t + 3 t + 6 t INI= , [6, 3, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-6*t^5-6*t^4+3*t^3+3*t^2+6*t)/(2*t^6-3*t^3+1) 21 20 19 18 17 INI= , [6, 4, 3], Generating Function=, (6 t - 6 t - 3 t + 4 t - 6 t 16 15 14 13 12 11 10 9 8 - 4 t - 4 t + 8 t - 3 t - 4 t + 2 t + 6 t + 3 t + 10 t 7 6 5 4 3 2 / 20 10 + 6 t + 4 t + 4 t + 6 t + 3 t + 4 t + 6 t) / (t - 2 t + 1) / and in Maple notation: (6*t^21-6*t^20-3*t^19+4*t^18-6*t^17-4*t^16-4*t^15+8*t^14-3*t^13-4*t^12+2*t^11+6 *t^10+3*t^9+10*t^8+6*t^7+4*t^6+4*t^5+6*t^4+3*t^3+4*t^2+6*t)/(t^20-2*t^10+1) INI= , [6, 5, 2], Generating Function=, 9 8 7 6 3 2 4 t - 5 t - 6 t + 6 t - 4 t + 5 t + 6 t --------------------------------------------- 8 6 2 t - t - t + 1 and in Maple notation: (4*t^9-5*t^8-6*t^7+6*t^6-4*t^3+5*t^2+6*t)/(t^8-t^6-t^2+1) 9 8 7 3 2 4 t - t - 6 t - 4 t + 7 t + 6 t INI= , [6, 7, 2], Generating Function=, ------------------------------------ 8 6 2 t - t - t + 1 and in Maple notation: (4*t^9-t^8-6*t^7-4*t^3+7*t^2+6*t)/(t^8-t^6-t^2+1) 11 3 2 -2 t - 4 t + 8 t + 6 t INI= , [6, 8, 2], Generating Function=, -------------------------- 10 8 2 t - t - t + 1 and in Maple notation: (-2*t^11-4*t^3+8*t^2+6*t)/(t^10-t^8-t^2+1) INI= , [6, 9, 2], Generating Function=, 10 9 8 7 3 2 6 t + 4 t - 9 t - 6 t - 4 t + 9 t + 6 t ---------------------------------------------- 8 6 2 t - t - t + 1 and in Maple notation: (6*t^10+4*t^9-9*t^8-6*t^7-4*t^3+9*t^2+6*t)/(t^8-t^6-t^2+1) 13 3 2 -2 t - 4 t + 10 t + 6 t INI= , [6, 10, 2], Generating Function=, --------------------------- 12 10 2 t - t - t + 1 and in Maple notation: (-2*t^13-4*t^3+10*t^2+6*t)/(t^12-t^10-t^2+1) 6 5 4 3 2 -6 t - 6 t - 7 t + 3 t + 3 t + 7 t INI= , [7, 3, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-6*t^5-7*t^4+3*t^3+3*t^2+7*t)/(2*t^6-3*t^3+1) 21 20 19 18 17 INI= , [7, 4, 3], Generating Function=, (6 t - 6 t - 3 t + 3 t - 6 t 16 15 14 13 12 11 10 9 8 - 4 t - 4 t + 7 t - 3 t - 4 t + t + 6 t + 3 t + 11 t 7 6 5 4 3 2 / 20 10 + 6 t + 4 t + 4 t + 7 t + 3 t + 4 t + 7 t) / (t - 2 t + 1) / and in Maple notation: (6*t^21-6*t^20-3*t^19+3*t^18-6*t^17-4*t^16-4*t^15+7*t^14-3*t^13-4*t^12+t^11+6*t ^10+3*t^9+11*t^8+6*t^7+4*t^6+4*t^5+7*t^4+3*t^3+4*t^2+7*t)/(t^20-2*t^10+1) 25 24 23 22 21 INI= , [7, 9, 2], Generating Function=, (-5 t + 7 t - 5 t + 7 t - 5 t 20 18 17 16 15 14 13 12 + 7 t + 7 t - 9 t + 12 t - 16 t + 12 t - 16 t + 12 t 11 10 9 8 7 6 5 4 3 2 - 16 t + 2 t + 2 t + 9 t + 2 t + 9 t + 2 t + 9 t + 2 t + 9 t / 18 9 + 7 t) / (t - 2 t + 1) / and in Maple notation: (-5*t^25+7*t^24-5*t^23+7*t^22-5*t^21+7*t^20+7*t^18-9*t^17+12*t^16-16*t^15+12*t^ 14-16*t^13+12*t^12-16*t^11+2*t^10+2*t^9+9*t^8+2*t^7+9*t^6+2*t^5+9*t^4+2*t^3+9*t ^2+7*t)/(t^18-2*t^9+1) 15 14 13 12 11 INI= , [8, 2, 1], Generating Function=, (3 t - 6 t - 4 t - t + 7 t 10 9 7 6 5 4 3 2 / + 6 t - 8 t - 3 t + 6 t + 4 t + t - 7 t + 2 t + 8 t) / ( / 10 8 2 t - t - t + 1) and in Maple notation: (3*t^15-6*t^14-4*t^13-t^12+7*t^11+6*t^10-8*t^9-3*t^7+6*t^6+4*t^5+t^4-7*t^3+2*t^ 2+8*t)/(t^10-t^8-t^2+1) 14 13 12 11 10 INI= , [8, 2, 2], Generating Function=, (2 t - 8 t - 2 t + 14 t - 2 t 9 6 5 4 3 2 / 10 8 2 - 8 t - 2 t + 8 t + 2 t - 6 t + 2 t + 8 t) / (t - t - t + 1) / and in Maple notation: (2*t^14-8*t^13-2*t^12+14*t^11-2*t^10-8*t^9-2*t^6+8*t^5+2*t^4-6*t^3+2*t^2+8*t)/( t^10-t^8-t^2+1) 26 25 24 23 22 INI= , [8, 2, 3], Generating Function=, (11 t - 7 t - t - 8 t - 8 t 21 20 19 18 17 16 15 14 13 + 13 t + 6 t - 8 t - 11 t + 7 t + t + 8 t + 8 t - 4 t 12 11 10 9 5 4 3 2 / - 14 t + 13 t - 2 t - 8 t - t + 8 t - 5 t + 2 t + 8 t) / ( / 10 8 2 t - t - t + 1) and in Maple notation: (11*t^26-7*t^25-t^24-8*t^23-8*t^22+13*t^21+6*t^20-8*t^19-11*t^18+7*t^17+t^16+8* t^15+8*t^14-4*t^13-14*t^12+13*t^11-2*t^10-8*t^9-t^5+8*t^4-5*t^3+2*t^2+8*t)/(t^ 10-t^8-t^2+1) INI= , [8, 2, 4], Generating Function=, 11 10 9 5 3 2 4 t - 2 t - 8 t + 8 t - 4 t + 2 t + 8 t ----------------------------------------------- 10 8 2 t - t - t + 1 and in Maple notation: (4*t^11-2*t^10-8*t^9+8*t^5-4*t^3+2*t^2+8*t)/(t^10-t^8-t^2+1) INI= , [8, 2, 6], Generating Function=, 11 10 9 7 3 2 2 t - 2 t - 8 t + 8 t - 2 t + 2 t + 8 t ----------------------------------------------- 10 8 2 t - t - t + 1 and in Maple notation: (2*t^11-2*t^10-8*t^9+8*t^7-2*t^3+2*t^2+8*t)/(t^10-t^8-t^2+1) 23 22 21 20 19 INI= , [8, 2, 7], Generating Function=, (7 t - 13 t + t + 6 t - 8 t 18 17 16 15 14 13 12 11 10 + 8 t + 5 t - 8 t - 7 t + 13 t - t - 6 t + 9 t - 2 t 9 8 3 2 / 10 8 2 - 13 t + 8 t - t + 2 t + 8 t) / (t - t - t + 1) / and in Maple notation: (7*t^23-13*t^22+t^21+6*t^20-8*t^19+8*t^18+5*t^17-8*t^16-7*t^15+13*t^14-t^13-6*t ^12+9*t^11-2*t^10-13*t^9+8*t^8-t^3+2*t^2+8*t)/(t^10-t^8-t^2+1) 10 2 -2 t + 2 t + 8 t INI= , [8, 2, 8], Generating Function=, ------------------- 10 8 2 t - t - t + 1 and in Maple notation: (-2*t^10+2*t^2+8*t)/(t^10-t^8-t^2+1) INI= , [8, 2, 10], Generating Function=, 11 10 9 3 2 6 t - 2 t - 8 t + 2 t + 2 t + 8 t ---------------------------------------- 10 8 2 t - t - t + 1 and in Maple notation: (6*t^11-2*t^10-8*t^9+2*t^3+2*t^2+8*t)/(t^10-t^8-t^2+1) INI= , [8, 3, 2], Generating Function=, 11 10 9 4 3 2 6 t - 3 t - 8 t + 8 t - 6 t + 3 t + 8 t ----------------------------------------------- 10 8 2 t - t - t + 1 and in Maple notation: (6*t^11-3*t^10-8*t^9+8*t^4-6*t^3+3*t^2+8*t)/(t^10-t^8-t^2+1) 6 5 4 3 2 -6 t - 6 t - 8 t + 3 t + 3 t + 8 t INI= , [8, 3, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-6*t^5-8*t^4+3*t^3+3*t^2+8*t)/(2*t^6-3*t^3+1) 21 20 19 18 17 INI= , [8, 4, 3], Generating Function=, (6 t - 6 t - 3 t + 2 t - 6 t 16 15 14 13 12 10 9 8 7 - 4 t - 4 t + 6 t - 3 t - 4 t + 6 t + 3 t + 12 t + 6 t 6 5 4 3 2 / 20 10 + 4 t + 4 t + 8 t + 3 t + 4 t + 8 t) / (t - 2 t + 1) / and in Maple notation: (6*t^21-6*t^20-3*t^19+2*t^18-6*t^17-4*t^16-4*t^15+6*t^14-3*t^13-4*t^12+6*t^10+3 *t^9+12*t^8+6*t^7+4*t^6+4*t^5+8*t^4+3*t^3+4*t^2+8*t)/(t^20-2*t^10+1) INI= , [8, 5, 2], Generating Function=, 11 10 9 6 3 2 6 t - 5 t - 8 t + 8 t - 6 t + 5 t + 8 t ----------------------------------------------- 10 8 2 t - t - t + 1 and in Maple notation: (6*t^11-5*t^10-8*t^9+8*t^6-6*t^3+5*t^2+8*t)/(t^10-t^8-t^2+1) INI= , [8, 7, 2], Generating Function=, 11 10 9 8 3 2 6 t - 7 t - 8 t + 8 t - 6 t + 7 t + 8 t ----------------------------------------------- 10 8 2 t - t - t + 1 and in Maple notation: (6*t^11-7*t^10-8*t^9+8*t^8-6*t^3+7*t^2+8*t)/(t^10-t^8-t^2+1) 11 10 9 3 2 6 t - t - 8 t - 6 t + 9 t + 8 t INI= , [8, 9, 2], Generating Function=, -------------------------------------- 10 8 2 t - t - t + 1 and in Maple notation: (6*t^11-t^10-8*t^9-6*t^3+9*t^2+8*t)/(t^10-t^8-t^2+1) 13 3 2 -2 t - 6 t + 10 t + 8 t INI= , [8, 10, 2], Generating Function=, --------------------------- 12 10 2 t - t - t + 1 and in Maple notation: (-2*t^13-6*t^3+10*t^2+8*t)/(t^12-t^10-t^2+1) 52 51 50 49 48 INI= , [9, 2, 7], Generating Function=, (11 t - 5 t - 2 t - 2 t + 2 t 47 46 45 44 43 42 41 40 39 - 7 t + 2 t + 9 t - 4 t - 11 t + 2 t - 2 t + 2 t - 2 t 38 37 36 35 34 33 32 31 29 + 2 t - 2 t + 2 t - 2 t + 2 t - 2 t + 11 t - 2 t + 20 t 27 26 24 23 22 21 20 19 - 5 t + 18 t + 18 t + 4 t + 4 t + 11 t + 20 t + 2 t 18 17 16 15 14 13 12 11 + 20 t + 2 t + 20 t + 2 t + 20 t + 2 t + 20 t + 2 t 10 9 8 7 6 5 4 3 2 + 11 t + 2 t + 11 t + 7 t + 2 t + 7 t + 2 t + 7 t + 2 t + 9 t) / 44 22 / (t - 2 t + 1) / and in Maple notation: (11*t^52-5*t^51-2*t^50-2*t^49+2*t^48-7*t^47+2*t^46+9*t^45-4*t^44-11*t^43+2*t^42 -2*t^41+2*t^40-2*t^39+2*t^38-2*t^37+2*t^36-2*t^35+2*t^34-2*t^33+11*t^32-2*t^31+ 20*t^29-5*t^27+18*t^26+18*t^24+4*t^23+4*t^22+11*t^21+20*t^20+2*t^19+20*t^18+2*t ^17+20*t^16+2*t^15+20*t^14+2*t^13+20*t^12+2*t^11+11*t^10+2*t^9+11*t^8+7*t^7+2*t ^6+7*t^5+2*t^4+7*t^3+2*t^2+9*t)/(t^44-2*t^22+1) 6 5 4 3 2 -6 t - 6 t - 9 t + 3 t + 3 t + 9 t INI= , [9, 3, 3], Generating Function=, --------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-6*t^5-9*t^4+3*t^3+3*t^2+9*t)/(2*t^6-3*t^3+1) 21 20 19 18 17 INI= , [9, 4, 3], Generating Function=, (6 t - 6 t - 3 t + t - 6 t 16 15 14 13 12 11 10 9 8 - 4 t - 4 t + 5 t - 3 t - 4 t - t + 6 t + 3 t + 13 t 7 6 5 4 3 2 / 20 10 + 6 t + 4 t + 4 t + 9 t + 3 t + 4 t + 9 t) / (t - 2 t + 1) / and in Maple notation: (6*t^21-6*t^20-3*t^19+t^18-6*t^17-4*t^16-4*t^15+5*t^14-3*t^13-4*t^12-t^11+6*t^ 10+3*t^9+13*t^8+6*t^7+4*t^6+4*t^5+9*t^4+3*t^3+4*t^2+9*t)/(t^20-2*t^10+1) 17 16 15 14 13 INI= , [10, 2, 1], Generating Function=, (3 t - 8 t - 4 t - t + 9 t 12 11 7 6 5 4 3 2 / + 8 t - 10 t - 3 t + 8 t + 4 t + t - 9 t + 2 t + 10 t) / ( / 12 10 2 t - t - t + 1) and in Maple notation: (3*t^17-8*t^16-4*t^15-t^14+9*t^13+8*t^12-10*t^11-3*t^7+8*t^6+4*t^5+t^4-9*t^3+2* t^2+10*t)/(t^12-t^10-t^2+1) 16 15 14 13 INI= , [10, 2, 2], Generating Function=, (2 t - 10 t - 2 t + 18 t 12 11 6 5 4 3 2 / - 2 t - 10 t - 2 t + 10 t + 2 t - 8 t + 2 t + 10 t) / ( / 12 10 2 t - t - t + 1) and in Maple notation: (2*t^16-10*t^15-2*t^14+18*t^13-2*t^12-10*t^11-2*t^6+10*t^5+2*t^4-8*t^3+2*t^2+10 *t)/(t^12-t^10-t^2+1) 30 29 28 27 INI= , [10, 2, 3], Generating Function=, (13 t - 9 t - t - 10 t 26 25 24 23 20 19 18 17 - 10 t + 17 t + 8 t - 10 t - 13 t + 9 t + t + 10 t 16 15 14 13 12 11 5 4 3 + 10 t - 6 t - 18 t + 17 t - 2 t - 10 t - t + 10 t - 7 t 2 / 12 10 2 + 2 t + 10 t) / (t - t - t + 1) / and in Maple notation: (13*t^30-9*t^29-t^28-10*t^27-10*t^26+17*t^25+8*t^24-10*t^23-13*t^20+9*t^19+t^18 +10*t^17+10*t^16-6*t^15-18*t^14+17*t^13-2*t^12-10*t^11-t^5+10*t^4-7*t^3+2*t^2+ 10*t)/(t^12-t^10-t^2+1) INI= , [10, 2, 4], Generating Function=, 13 12 11 5 3 2 6 t - 2 t - 10 t + 10 t - 6 t + 2 t + 10 t --------------------------------------------------- 12 10 2 t - t - t + 1 and in Maple notation: (6*t^13-2*t^12-10*t^11+10*t^5-6*t^3+2*t^2+10*t)/(t^12-t^10-t^2+1) INI= , [10, 2, 6], Generating Function=, 13 12 11 7 3 2 4 t - 2 t - 10 t + 10 t - 4 t + 2 t + 10 t --------------------------------------------------- 12 10 2 t - t - t + 1 and in Maple notation: (4*t^13-2*t^12-10*t^11+10*t^7-4*t^3+2*t^2+10*t)/(t^12-t^10-t^2+1) INI= , [10, 2, 8], Generating Function=, 13 12 11 9 3 2 2 t - 2 t - 10 t + 10 t - 2 t + 2 t + 10 t --------------------------------------------------- 12 10 2 t - t - t + 1 and in Maple notation: (2*t^13-2*t^12-10*t^11+10*t^9-2*t^3+2*t^2+10*t)/(t^12-t^10-t^2+1) 27 26 25 24 23 INI= , [10, 2, 9], Generating Function=, (9 t - 17 t + t + 8 t - 10 t 22 21 20 17 16 15 14 13 12 + 10 t + 7 t - 10 t - 9 t + 17 t - t - 8 t + 11 t - 2 t 11 10 3 2 / 12 10 2 - 17 t + 10 t - t + 2 t + 10 t) / (t - t - t + 1) / and in Maple notation: (9*t^27-17*t^26+t^25+8*t^24-10*t^23+10*t^22+7*t^21-10*t^20-9*t^17+17*t^16-t^15-\ 8*t^14+11*t^13-2*t^12-17*t^11+10*t^10-t^3+2*t^2+10*t)/(t^12-t^10-t^2+1) 12 2 -2 t + 2 t + 10 t INI= , [10, 2, 10], Generating Function=, -------------------- 12 10 2 t - t - t + 1 and in Maple notation: (-2*t^12+2*t^2+10*t)/(t^12-t^10-t^2+1) INI= , [10, 3, 2], Generating Function=, 13 12 11 4 3 2 8 t - 3 t - 10 t + 10 t - 8 t + 3 t + 10 t --------------------------------------------------- 12 10 2 t - t - t + 1 and in Maple notation: (8*t^13-3*t^12-10*t^11+10*t^4-8*t^3+3*t^2+10*t)/(t^12-t^10-t^2+1) INI= , [10, 3, 3], Generating Function=, 6 5 4 3 2 -6 t - 6 t - 10 t + 3 t + 3 t + 10 t ----------------------------------------- 6 3 2 t - 3 t + 1 and in Maple notation: (-6*t^6-6*t^5-10*t^4+3*t^3+3*t^2+10*t)/(2*t^6-3*t^3+1) 21 20 19 17 16 INI= , [10, 4, 3], Generating Function=, (6 t - 6 t - 3 t - 6 t - 4 t 15 14 13 12 11 10 9 8 7 - 4 t + 4 t - 3 t - 4 t - 2 t + 6 t + 3 t + 14 t + 6 t 6 5 4 3 2 / 20 10 + 4 t + 4 t + 10 t + 3 t + 4 t + 10 t) / (t - 2 t + 1) / and in Maple notation: (6*t^21-6*t^20-3*t^19-6*t^17-4*t^16-4*t^15+4*t^14-3*t^13-4*t^12-2*t^11+6*t^10+3 *t^9+14*t^8+6*t^7+4*t^6+4*t^5+10*t^4+3*t^3+4*t^2+10*t)/(t^20-2*t^10+1) INI= , [10, 5, 2], Generating Function=, 13 12 11 6 3 2 8 t - 5 t - 10 t + 10 t - 8 t + 5 t + 10 t --------------------------------------------------- 12 10 2 t - t - t + 1 and in Maple notation: (8*t^13-5*t^12-10*t^11+10*t^6-8*t^3+5*t^2+10*t)/(t^12-t^10-t^2+1) INI= , [10, 7, 2], Generating Function=, 13 12 11 8 3 2 8 t - 7 t - 10 t + 10 t - 8 t + 7 t + 10 t --------------------------------------------------- 12 10 2 t - t - t + 1 and in Maple notation: (8*t^13-7*t^12-10*t^11+10*t^8-8*t^3+7*t^2+10*t)/(t^12-t^10-t^2+1) INI= , [10, 9, 2], Generating Function=, 13 12 11 10 3 2 8 t - 9 t - 10 t + 10 t - 8 t + 9 t + 10 t ---------------------------------------------------- 12 10 2 t - t - t + 1 and in Maple notation: (8*t^13-9*t^12-10*t^11+10*t^10-8*t^3+9*t^2+10*t)/(t^12-t^10-t^2+1) To sum up, here are the succesful ones, in Maple notation. {[[1, 1, 3], (-t^17-4*t^14+t^13-t^12-3*t^11-2*t^10-t^9+t^8-5*t^7-t^6+2*t^4+3*t^ 3+t^2+t)/(t^9-2*t^3+1)], [[1, 3, 2], (t^6-3*t^5+2*t^4+2*t^3+3*t^2+t)/(t^6-2*t^3 +1)], [[2, 1, 3], (-3*t^6-t^5+t^4+3*t^3+t^2+2*t)/(t^6-2*t^3+1)], [[2, 1, 4], (-\ 2*t^9+2*t^8+4*t^7-5*t^6-2*t^5+2*t^4+t^2+2*t)/(t^4-2*t^2+1)], [[2, 2, 4], (-2*t^ 4+2*t^2+2*t)/(t^4-2*t^2+1)], [[2, 2, 6], (2*t^7-4*t^5-2*t^4+2*t^3+2*t^2+2*t)/(t ^4-2*t^2+1)], [[2, 2, 8], (2*t^9-6*t^5-2*t^4+4*t^3+2*t^2+2*t)/(t^4-2*t^2+1)], [ [2, 2, 10], (2*t^11-8*t^5-2*t^4+6*t^3+2*t^2+2*t)/(t^4-2*t^2+1)], [[2, 3, 1], (- t^7-t^6-t^4+t^3+3*t^2+2*t)/(t^6-2*t^3+1)], [[2, 3, 2], (-t^4-2*t^3+3*t^2+2*t)/( t^4-2*t^2+1)], [[2, 3, 4], (t^6-4*t^4+3*t^2+2*t)/(t^4-2*t^2+1)], [[2, 3, 5], (2 *t^10-t^9-4*t^8+3*t^7+3*t^6-3*t^5-4*t^4+t^3+3*t^2+2*t)/(t^4-2*t^2+1)], [[2, 3, 6], (2*t^7+t^6-4*t^5-4*t^4+2*t^3+3*t^2+2*t)/(t^4-2*t^2+1)], [[2, 3, 7], (2*t^12 -t^11-4*t^10+3*t^9+2*t^8+t^6-5*t^5-4*t^4+3*t^3+3*t^2+2*t)/(t^4-2*t^2+1)], [[2, 3, 8], (2*t^9+t^6-6*t^5-4*t^4+4*t^3+3*t^2+2*t)/(t^4-2*t^2+1)], [[2, 3, 9], (2*t ^14-t^13-4*t^12+3*t^11+2*t^10+t^6-7*t^5-4*t^4+5*t^3+3*t^2+2*t)/(t^4-2*t^2+1)], [[2, 3, 10], (2*t^11+t^6-8*t^5-4*t^4+6*t^3+3*t^2+2*t)/(t^4-2*t^2+1)], [[2, 4, 2 ], (-2*t^7+4*t^2+2*t)/(t^6-t^4-t^2+1)], [[2, 4, 3], (-2*t^10+4*t^8-t^7-4*t^6+2* t^5-2*t^4+t^3+4*t^2+2*t)/(t^6-t^4-t^2+1)], [[2, 5, 2], (2*t^6-5*t^4-2*t^3+5*t^2 +2*t)/(t^4-2*t^2+1)], [[2, 5, 3], (2*t^9-5*t^7+3*t^6+4*t^5-8*t^4-t^3+5*t^2+2*t) /(t^4-2*t^2+1)], [[2, 6, 2], (-2*t^9+6*t^2+2*t)/(t^8-t^6-t^2+1)], [[2, 6, 3], ( -2*t^12+6*t^10-t^9-6*t^8-2*t^7+6*t^5-4*t^4+t^3+6*t^2+2*t)/(t^8-t^6-t^2+1)], [[2 , 7, 2], (2*t^8-7*t^4-2*t^3+7*t^2+2*t)/(t^4-2*t^2+1)], [[2, 7, 3], (2*t^11-7*t^ 7+5*t^6+6*t^5-12*t^4-t^3+7*t^2+2*t)/(t^4-2*t^2+1)], [[2, 8, 2], (-2*t^11+8*t^2+ 2*t)/(t^10-t^8-t^2+1)], [[2, 8, 3], (-2*t^14+8*t^12-t^11-8*t^10-2*t^9+8*t^5-6*t ^4+t^3+8*t^2+2*t)/(t^10-t^8-t^2+1)], [[2, 9, 2], (2*t^10-9*t^4-2*t^3+9*t^2+2*t) /(t^4-2*t^2+1)], [[2, 9, 3], (2*t^13-9*t^7+7*t^6+8*t^5-16*t^4-t^3+9*t^2+2*t)/(t ^4-2*t^2+1)], [[2, 10, 2], (-2*t^13+10*t^2+2*t)/(t^12-t^10-t^2+1)], [[2, 10, 3] , (-2*t^16+10*t^14-t^13-10*t^12-2*t^11+10*t^5-8*t^4+t^3+10*t^2+2*t)/(t^12-t^10- t^2+1)], [[3, 2, 1], (2*t^6+t^5-3*t^4+t^3+2*t^2+3*t)/(t^6-2*t^3+1)], [[3, 3, 3] , (-6*t^6-6*t^5-3*t^4+3*t^3+3*t^2+3*t)/(2*t^6-3*t^3+1)], [[3, 3, 5], (-5*t^6-6* t^5-6*t^4+5*t^3+3*t^2+3*t)/(2*t^6-3*t^3+1)], [[3, 3, 6], (-6*t^6-6*t^5-6*t^4+6* t^3+3*t^2+3*t)/(2*t^6-3*t^3+1)], [[3, 3, 7], (-7*t^6-6*t^5-6*t^4+7*t^3+3*t^2+3* t)/(2*t^6-3*t^3+1)], [[3, 3, 8], (-8*t^6-6*t^5-6*t^4+8*t^3+3*t^2+3*t)/(2*t^6-3* t^3+1)], [[3, 3, 9], (-9*t^6-6*t^5-6*t^4+9*t^3+3*t^2+3*t)/(2*t^6-3*t^3+1)], [[3 , 3, 10], (-10*t^6-6*t^5-6*t^4+10*t^3+3*t^2+3*t)/(2*t^6-3*t^3+1)], [[3, 4, 3], (-6*t^6-4*t^5-6*t^4+3*t^3+4*t^2+3*t)/(2*t^6-3*t^3+1)], [[3, 5, 2], (-t^13+3*t^ 12+3*t^10-5*t^9+4*t^8-8*t^7+2*t^6+2*t^5+5*t^4+2*t^3+5*t^2+3*t)/(t^10-2*t^5+1)], [[3, 5, 3], (-6*t^6-5*t^5-6*t^4+3*t^3+5*t^2+3*t)/(2*t^6-3*t^3+1)], [[3, 6, 3], (-6*t^6-6*t^5-6*t^4+3*t^3+6*t^2+3*t)/(2*t^6-3*t^3+1)], [[3, 7, 3], (-6*t^6-7*t^ 5-6*t^4+3*t^3+7*t^2+3*t)/(2*t^6-3*t^3+1)], [[3, 8, 3], (-6*t^6-8*t^5-6*t^4+3*t^ 3+8*t^2+3*t)/(2*t^6-3*t^3+1)], [[3, 9, 3], (-6*t^6-9*t^5-6*t^4+3*t^3+9*t^2+3*t) /(2*t^6-3*t^3+1)], [[3, 10, 3], (-6*t^6-10*t^5-6*t^4+3*t^3+10*t^2+3*t)/(2*t^6-3 *t^3+1)], [[4, 2, 2], (2*t^10-4*t^9-2*t^8+6*t^7-4*t^6+2*t^4-2*t^3+2*t^2+4*t)/(t ^6-t^4-t^2+1)], [[4, 2, 4], (-2*t^6+2*t^2+4*t)/(t^6-t^4-t^2+1)], [[4, 2, 6], (2 *t^7-2*t^6-4*t^5+2*t^3+2*t^2+4*t)/(t^6-t^4-t^2+1)], [[4, 2, 8], (4*t^9-4*t^7-2* t^6-4*t^5+4*t^3+2*t^2+4*t)/(t^6-t^4-t^2+1)], [[4, 2, 10], (4*t^11-6*t^7-2*t^6-4 *t^5+6*t^3+2*t^2+4*t)/(t^6-t^4-t^2+1)], [[4, 3, 2], (2*t^7-3*t^6-4*t^5+4*t^4-2* t^3+3*t^2+4*t)/(t^6-t^4-t^2+1)], [[4, 3, 3], (-6*t^6-6*t^5-4*t^4+3*t^3+3*t^2+4* t)/(2*t^6-3*t^3+1)], [[4, 3, 5], (t^20-6*t^19-3*t^18+5*t^17-6*t^16-4*t^15-4*t^ 14+9*t^13-3*t^12-4*t^11+13*t^10+6*t^9+3*t^8+9*t^7+6*t^6+4*t^5+4*t^4+5*t^3+3*t^2 +4*t)/(t^20-2*t^10+1)], [[4, 3, 6], (-6*t^19-3*t^18+4*t^17-6*t^16-4*t^15-4*t^14 +8*t^13-3*t^12-4*t^11+14*t^10+6*t^9+3*t^8+10*t^7+6*t^6+4*t^5+4*t^4+6*t^3+3*t^2+ 4*t)/(t^20-2*t^10+1)], [[4, 3, 7], (-t^20-6*t^19-3*t^18+3*t^17-6*t^16-4*t^15-4* t^14+7*t^13-3*t^12-4*t^11+15*t^10+6*t^9+3*t^8+11*t^7+6*t^6+4*t^5+4*t^4+7*t^3+3* t^2+4*t)/(t^20-2*t^10+1)], [[4, 3, 8], (-2*t^20-6*t^19-3*t^18+2*t^17-6*t^16-4*t ^15-4*t^14+6*t^13-3*t^12-4*t^11+16*t^10+6*t^9+3*t^8+12*t^7+6*t^6+4*t^5+4*t^4+8* t^3+3*t^2+4*t)/(t^20-2*t^10+1)], [[4, 3, 9], (-3*t^20-6*t^19-3*t^18+t^17-6*t^16 -4*t^15-4*t^14+5*t^13-3*t^12-4*t^11+17*t^10+6*t^9+3*t^8+13*t^7+6*t^6+4*t^5+4*t^ 4+9*t^3+3*t^2+4*t)/(t^20-2*t^10+1)], [[4, 3, 10], (-4*t^20-6*t^19-3*t^18-6*t^16 -4*t^15-4*t^14+4*t^13-3*t^12-4*t^11+18*t^10+6*t^9+3*t^8+14*t^7+6*t^6+4*t^5+4*t^ 4+10*t^3+3*t^2+4*t)/(t^20-2*t^10+1)], [[4, 4, 3], (2*t^25-2*t^24+2*t^22-2*t^21-\ 4*t^20-4*t^19+2*t^18-3*t^17-4*t^16+4*t^15-2*t^14-3*t^13+8*t^12-2*t^11+4*t^10+4* t^9+12*t^8+3*t^7+4*t^6+8*t^5+4*t^4+3*t^3+4*t^2+4*t)/(t^20-2*t^10+1)], [[4, 5, 2 ], (2*t^7-t^6-4*t^5-2*t^3+5*t^2+4*t)/(t^6-t^4-t^2+1)], [[4, 6, 2], (-2*t^9-2*t^ 3+6*t^2+4*t)/(t^8-t^6-t^2+1)], [[4, 7, 2], (4*t^8+2*t^7-7*t^6-4*t^5-2*t^3+7*t^2 +4*t)/(t^6-t^4-t^2+1)], [[4, 8, 2], (-2*t^11-2*t^3+8*t^2+4*t)/(t^10-t^8-t^2+1)] , [[4, 9, 2], (4*t^10+2*t^7-9*t^6-4*t^5-2*t^3+9*t^2+4*t)/(t^6-t^4-t^2+1)], [[4, 10, 2], (-2*t^13-2*t^3+10*t^2+4*t)/(t^12-t^10-t^2+1)], [[5, 3, 3], (-6*t^6-6*t^ 5-5*t^4+3*t^3+3*t^2+5*t)/(2*t^6-3*t^3+1)], [[5, 7, 2], (-3*t^19+5*t^18-3*t^17+5 *t^16+5*t^14-7*t^13+8*t^12-12*t^11+8*t^10-12*t^9+2*t^8+2*t^7+7*t^6+2*t^5+7*t^4+ 2*t^3+7*t^2+5*t)/(t^14-2*t^7+1)], [[6, 2, 1], (3*t^13-4*t^12-4*t^11-t^10+5*t^9+ 4*t^8-9*t^7+4*t^6+4*t^5+t^4-5*t^3+2*t^2+6*t)/(t^8-t^6-t^2+1)], [[6, 2, 2], (2*t ^12-6*t^11-2*t^10+10*t^9-2*t^8-6*t^7-2*t^6+6*t^5+2*t^4-4*t^3+2*t^2+6*t)/(t^8-t^ 6-t^2+1)], [[6, 2, 3], (9*t^22-5*t^21-t^20-6*t^19-6*t^18+9*t^17-5*t^16-t^15+t^ 14+6*t^13+6*t^12-2*t^11-10*t^10+9*t^9-2*t^8-6*t^7-t^5+6*t^4-3*t^3+2*t^2+6*t)/(t ^8-t^6-t^2+1)], [[6, 2, 4], (2*t^9-2*t^8-6*t^7+6*t^5-2*t^3+2*t^2+6*t)/(t^8-t^6- t^2+1)], [[6, 2, 5], (49*t^61-41*t^60-25*t^59+18*t^58+8*t^56-54*t^55+39*t^54+26 *t^53-27*t^52+3*t^51-7*t^50-6*t^49+34*t^48+12*t^47-37*t^46-12*t^45+43*t^44+2*t^ 43-59*t^42+10*t^41+46*t^40-8*t^39-24*t^38+6*t^37+16*t^36-11*t^35-8*t^34+6*t^33-\ 2*t^32+7*t^30-4*t^29-6*t^28+6*t^27-2*t^24-10*t^23+18*t^22+5*t^21-13*t^20+2*t^19 -3*t^18+3*t^17-6*t^15+t^14+4*t^13+3*t^12-t^11-4*t^10+7*t^9-2*t^8-9*t^7+6*t^6-t^ 3+2*t^2+6*t)/(t^8-t^6-t^2+1)], [[6, 2, 6], (-2*t^8+2*t^2+6*t)/(t^8-t^6-t^2+1)], [[6, 2, 7], (14*t^28-18*t^27-t^26+11*t^25-6*t^24+t^23-14*t^22+15*t^21-4*t^19+2* t^18-t^17+4*t^16+2*t^15-5*t^14-7*t^13+4*t^12+6*t^11-4*t^10+4*t^8-6*t^7+t^3+2*t^ 2+6*t)/(t^8-t^6-t^2+1)], [[6, 2, 8], (4*t^9-2*t^8-6*t^7+2*t^3+2*t^2+6*t)/(t^8-t ^6-t^2+1)], [[6, 2, 10], (6*t^11-4*t^9-2*t^8-6*t^7+4*t^3+2*t^2+6*t)/(t^8-t^6-t^ 2+1)], [[6, 3, 2], (4*t^9-3*t^8-6*t^7+6*t^4-4*t^3+3*t^2+6*t)/(t^8-t^6-t^2+1)], [[6, 3, 3], (-6*t^6-6*t^5-6*t^4+3*t^3+3*t^2+6*t)/(2*t^6-3*t^3+1)], [[6, 4, 3], (6*t^21-6*t^20-3*t^19+4*t^18-6*t^17-4*t^16-4*t^15+8*t^14-3*t^13-4*t^12+2*t^11+6 *t^10+3*t^9+10*t^8+6*t^7+4*t^6+4*t^5+6*t^4+3*t^3+4*t^2+6*t)/(t^20-2*t^10+1)], [ [6, 5, 2], (4*t^9-5*t^8-6*t^7+6*t^6-4*t^3+5*t^2+6*t)/(t^8-t^6-t^2+1)], [[6, 7, 2], (4*t^9-t^8-6*t^7-4*t^3+7*t^2+6*t)/(t^8-t^6-t^2+1)], [[6, 8, 2], (-2*t^11-4* t^3+8*t^2+6*t)/(t^10-t^8-t^2+1)], [[6, 9, 2], (6*t^10+4*t^9-9*t^8-6*t^7-4*t^3+9 *t^2+6*t)/(t^8-t^6-t^2+1)], [[6, 10, 2], (-2*t^13-4*t^3+10*t^2+6*t)/(t^12-t^10- t^2+1)], [[7, 3, 3], (-6*t^6-6*t^5-7*t^4+3*t^3+3*t^2+7*t)/(2*t^6-3*t^3+1)], [[7 , 4, 3], (6*t^21-6*t^20-3*t^19+3*t^18-6*t^17-4*t^16-4*t^15+7*t^14-3*t^13-4*t^12 +t^11+6*t^10+3*t^9+11*t^8+6*t^7+4*t^6+4*t^5+7*t^4+3*t^3+4*t^2+7*t)/(t^20-2*t^10 +1)], [[7, 9, 2], (-5*t^25+7*t^24-5*t^23+7*t^22-5*t^21+7*t^20+7*t^18-9*t^17+12* t^16-16*t^15+12*t^14-16*t^13+12*t^12-16*t^11+2*t^10+2*t^9+9*t^8+2*t^7+9*t^6+2*t ^5+9*t^4+2*t^3+9*t^2+7*t)/(t^18-2*t^9+1)], [[8, 2, 1], (3*t^15-6*t^14-4*t^13-t^ 12+7*t^11+6*t^10-8*t^9-3*t^7+6*t^6+4*t^5+t^4-7*t^3+2*t^2+8*t)/(t^10-t^8-t^2+1)] , [[8, 2, 2], (2*t^14-8*t^13-2*t^12+14*t^11-2*t^10-8*t^9-2*t^6+8*t^5+2*t^4-6*t^ 3+2*t^2+8*t)/(t^10-t^8-t^2+1)], [[8, 2, 3], (11*t^26-7*t^25-t^24-8*t^23-8*t^22+ 13*t^21+6*t^20-8*t^19-11*t^18+7*t^17+t^16+8*t^15+8*t^14-4*t^13-14*t^12+13*t^11-\ 2*t^10-8*t^9-t^5+8*t^4-5*t^3+2*t^2+8*t)/(t^10-t^8-t^2+1)], [[8, 2, 4], (4*t^11-\ 2*t^10-8*t^9+8*t^5-4*t^3+2*t^2+8*t)/(t^10-t^8-t^2+1)], [[8, 2, 6], (2*t^11-2*t^ 10-8*t^9+8*t^7-2*t^3+2*t^2+8*t)/(t^10-t^8-t^2+1)], [[8, 2, 7], (7*t^23-13*t^22+ t^21+6*t^20-8*t^19+8*t^18+5*t^17-8*t^16-7*t^15+13*t^14-t^13-6*t^12+9*t^11-2*t^ 10-13*t^9+8*t^8-t^3+2*t^2+8*t)/(t^10-t^8-t^2+1)], [[8, 2, 8], (-2*t^10+2*t^2+8* t)/(t^10-t^8-t^2+1)], [[8, 2, 10], (6*t^11-2*t^10-8*t^9+2*t^3+2*t^2+8*t)/(t^10- t^8-t^2+1)], [[8, 3, 2], (6*t^11-3*t^10-8*t^9+8*t^4-6*t^3+3*t^2+8*t)/(t^10-t^8- t^2+1)], [[8, 3, 3], (-6*t^6-6*t^5-8*t^4+3*t^3+3*t^2+8*t)/(2*t^6-3*t^3+1)], [[8 , 4, 3], (6*t^21-6*t^20-3*t^19+2*t^18-6*t^17-4*t^16-4*t^15+6*t^14-3*t^13-4*t^12 +6*t^10+3*t^9+12*t^8+6*t^7+4*t^6+4*t^5+8*t^4+3*t^3+4*t^2+8*t)/(t^20-2*t^10+1)], [[8, 5, 2], (6*t^11-5*t^10-8*t^9+8*t^6-6*t^3+5*t^2+8*t)/(t^10-t^8-t^2+1)], [[8, 7, 2], (6*t^11-7*t^10-8*t^9+8*t^8-6*t^3+7*t^2+8*t)/(t^10-t^8-t^2+1)], [[8, 9, 2 ], (6*t^11-t^10-8*t^9-6*t^3+9*t^2+8*t)/(t^10-t^8-t^2+1)], [[8, 10, 2], (-2*t^13 -6*t^3+10*t^2+8*t)/(t^12-t^10-t^2+1)], [[9, 2, 7], (11*t^52-5*t^51-2*t^50-2*t^ 49+2*t^48-7*t^47+2*t^46+9*t^45-4*t^44-11*t^43+2*t^42-2*t^41+2*t^40-2*t^39+2*t^ 38-2*t^37+2*t^36-2*t^35+2*t^34-2*t^33+11*t^32-2*t^31+20*t^29-5*t^27+18*t^26+18* t^24+4*t^23+4*t^22+11*t^21+20*t^20+2*t^19+20*t^18+2*t^17+20*t^16+2*t^15+20*t^14 +2*t^13+20*t^12+2*t^11+11*t^10+2*t^9+11*t^8+7*t^7+2*t^6+7*t^5+2*t^4+7*t^3+2*t^2 +9*t)/(t^44-2*t^22+1)], [[9, 3, 3], (-6*t^6-6*t^5-9*t^4+3*t^3+3*t^2+9*t)/(2*t^6 -3*t^3+1)], [[9, 4, 3], (6*t^21-6*t^20-3*t^19+t^18-6*t^17-4*t^16-4*t^15+5*t^14-\ 3*t^13-4*t^12-t^11+6*t^10+3*t^9+13*t^8+6*t^7+4*t^6+4*t^5+9*t^4+3*t^3+4*t^2+9*t) /(t^20-2*t^10+1)], [[10, 2, 1], (3*t^17-8*t^16-4*t^15-t^14+9*t^13+8*t^12-10*t^ 11-3*t^7+8*t^6+4*t^5+t^4-9*t^3+2*t^2+10*t)/(t^12-t^10-t^2+1)], [[10, 2, 2], (2* t^16-10*t^15-2*t^14+18*t^13-2*t^12-10*t^11-2*t^6+10*t^5+2*t^4-8*t^3+2*t^2+10*t) /(t^12-t^10-t^2+1)], [[10, 2, 3], (13*t^30-9*t^29-t^28-10*t^27-10*t^26+17*t^25+ 8*t^24-10*t^23-13*t^20+9*t^19+t^18+10*t^17+10*t^16-6*t^15-18*t^14+17*t^13-2*t^ 12-10*t^11-t^5+10*t^4-7*t^3+2*t^2+10*t)/(t^12-t^10-t^2+1)], [[10, 2, 4], (6*t^ 13-2*t^12-10*t^11+10*t^5-6*t^3+2*t^2+10*t)/(t^12-t^10-t^2+1)], [[10, 2, 6], (4* t^13-2*t^12-10*t^11+10*t^7-4*t^3+2*t^2+10*t)/(t^12-t^10-t^2+1)], [[10, 2, 8], ( 2*t^13-2*t^12-10*t^11+10*t^9-2*t^3+2*t^2+10*t)/(t^12-t^10-t^2+1)], [[10, 2, 9], (9*t^27-17*t^26+t^25+8*t^24-10*t^23+10*t^22+7*t^21-10*t^20-9*t^17+17*t^16-t^15-\ 8*t^14+11*t^13-2*t^12-17*t^11+10*t^10-t^3+2*t^2+10*t)/(t^12-t^10-t^2+1)], [[10, 2, 10], (-2*t^12+2*t^2+10*t)/(t^12-t^10-t^2+1)], [[10, 3, 2], (8*t^13-3*t^12-10 *t^11+10*t^4-8*t^3+3*t^2+10*t)/(t^12-t^10-t^2+1)], [[10, 3, 3], (-6*t^6-6*t^5-\ 10*t^4+3*t^3+3*t^2+10*t)/(2*t^6-3*t^3+1)], [[10, 4, 3], (6*t^21-6*t^20-3*t^19-6 *t^17-4*t^16-4*t^15+4*t^14-3*t^13-4*t^12-2*t^11+6*t^10+3*t^9+14*t^8+6*t^7+4*t^6 +4*t^5+10*t^4+3*t^3+4*t^2+10*t)/(t^20-2*t^10+1)], [[10, 5, 2], (8*t^13-5*t^12-\ 10*t^11+10*t^6-8*t^3+5*t^2+10*t)/(t^12-t^10-t^2+1)], [[10, 7, 2], (8*t^13-7*t^ 12-10*t^11+10*t^8-8*t^3+7*t^2+10*t)/(t^12-t^10-t^2+1)], [[10, 9, 2], (8*t^13-9* t^12-10*t^11+10*t^10-8*t^3+9*t^2+10*t)/(t^12-t^10-t^2+1)]} ----------------------------------------------------------------- This ends this article, that took, 1409.697, seconds.