#ComboProject 5
#Taerim Kim, Karnaa Mistry,Weij Zheng
#Results for AllTTT3: (3 x n) TicTacToe that ended in a tie

#The first 100 Terms of (3 x n) TicTacToe that ended in a tie
	
[3, 18, 16, 28, 30, 58, 72, 140, 178, 334, 444, 824, 1114, 2038, 2808, 5084, 7098, 12730, 17984, 32004, 45656, 80694, 116106, 204004, 295718, 516902, 754226, 1312336, 1926060, 3337682, 4924188, 8502132, 12602416, 21688182, 32284214, 55395140, 82777240, 141651742, 212415744, 362601356, 545495716, 929084578, 1401849594, 2382677360, 3604921774, 6115461118, 9275890122, 15707982020, 23881602058, 40375223374, 61518226734, 103846409504, 158548607640, 267258086338, 408814563524, 688201711116, 1054590179342, 1773088924494, 2721595930404, 4570470994288, 7026452822306, 11786751779582, 18147298366496, 30410128418476, 46885946293214, 78491476931042, 121177055746484, 202673497935940, 313283723643176, 523519086359942, 810192535596110, 1352760031582228, 2095874778731180, 3496664189134382, 5423295440740724, 9041173778178964, 14037073630916630, 23384428848794786, 36341276369869088, 60499749888807004, 94108595062116434, 156566731477339958, 243758321258056460, 405283671490379824, 631519064376051686, 1049367045483832694, 1636463783015528228, 2717688845726315884, 4241461650592403456, 7039983457241205026, 10995384407887915850, 18240595604152327816, 28509377078588235950, 47271347877169364534, 73934029147665383810, 122530697638498164244, 191768567416391711378, 317670103810998296390, 497489711804340577094, 823737936282279883384]

#Time for the computation
0.0620000000

#Recurence for the integer sequence and its initial conditions

-32*(n - 3)*(n - 5)*(6202880*n^2 + 291473253*n + 1931309011)*a(n)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) - 4*(140515804*n^4 + 1250607669*n^3 - 6973604044*n^2 - 5140067328*n - 35016172272)*a(n + 1)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) + 2*(966344545*n^4 + 27494409369*n^3 + 99502400168*n^2 - 576586974864*n + 285818855832)*a(n + 2)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) - (222848359*n^4 + 38533533290*n^3 + 593820247760*n^2 + 1433719231456*n - 2912585422944)*a(n + 3)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) - 2*(1337212610*n^4 + 30405404253*n^3 + 156236327320*n^2 - 648929441424*n - 2095594016352)*a(n + 4)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) + 2*(1909038007*n^4 + 57353364379*n^3 + 612038705456*n^2 + 2027861313680*n - 1098568362576)*a(n + 5)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) - 2*(511901590*n^4 + 13611445141*n^3 + 106185705128*n^2 + 427711340704*n + 831530669888)*a(n + 6)/((n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) + 2*(1346974791*n^4 + 53776735007*n^3 + 667854690984*n^2 + 3264541800400*n + 7778185196160)*a(n + 7)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) - 4*(99246080*n^4 + 10813335579*n^3 + 162605191456*n^2 + 185781831912*n - 3547559158320)*a(n + 8)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) - 16*(70257902*n^4 - 110072840*n^3 - 41006430749*n^2 - 467853221524*n - 1043018338974)*a(n + 9)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) + 2*(1337212610*n^4 + 41548801851*n^3 + 496145044696*n^2 + 2208298707984*n - 758231146848)*a(n + 10)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) - 2*(1909038007*n^4 + 66085865035*n^3 + 865726287680*n^2 + 5527399918736*n + 13765599752112)*a(n + 11)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) + 2*(1634950850*n^4 + 55901678819*n^3 + 476527769224*n^2 - 454619750288*n - 8727198170352)*a(n + 12)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) - 2*(1065943183*n^4 + 55732731761*n^3 + 954037359536*n^2 + 5780967220528*n + 7315610693760)*a(n + 13)/(3*(n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) - 2*(n + 21)*(255950795*n^3 + 4027991904*n^2 + 7775613176*n - 47095306360)*a(n + 14)/((n + 22)*(448991597*n^3 + 11172782648*n^2 + 84053262128*n + 137306722560)) + a(n + 15) = 0
a(1) = 16, a(2) = 30, a(3) = 72, a(4) = 178, a(5) = 444, a(6) = 1114, a(7) = 2808

a(1) = 3, a(2) = 18, a(3) = 16, a(4) = 28, a(5) = 30, a(6) = 58, a(7) = 72, a(8) = 140, a(9) = 178, a(10) = 334, a(11) = 444, a(12) = 824, a(13) = 1114, a(14) = 2038, a(15) = 2808

#Coherence with seq(nops(TicB(i,3,3)),i=1..6) #brutal process 
#in the first 6 terms
#note: TicB is suggested to be very inefficient after 7th term