--------------------------------------- n (n x) This for the curve for the limit of the log of the coefficient of, t w , 1 divided by n, in the rational function, ------------- 2 -t w - t + 1 + HHHHHHHHHHHHH + HHHHH HHHHH 0.45 HHH HHHH + HHH HH + HHH HH + HH HH 0.4 HH HH + HH HH + H HH 0.35 HH HH + HHH H + HH HH + H H 0.3 HH H + HH H + HH H + HH H 0.25H HH + H + H 0.2---+--+---+---+--+---+--+---+---+--+---+--+---+---+--+---+---+--+---+--+-*- 0.1 0.2 0.3 0.4 This took, 6.324, seconds. -------------------------------------------------- n (n x) This for the curve for the limit of the log of the coefficient of, t w , 1 divided by n, in the rational function, ------------- 1 - (w + 1) t 0.7 HHHHHHHHHHHH + HHHHH HHHHH + HHHH HHHH + HHH HH 0.6 HHH HHH + HHH HHH + HH HH + HH HH + HH HH 0.5 HH HH + HH HH + HH HH + HH HH 0.4 HH HH + HH HH + HH HH + HH HH + HH HH 0.3 H H + HH HH +**+--+--+---+--+--+---+--+--+--+---+--+--+---+--+--+---+--+--+---+--+--+**- 0.2 0.4 0.6 0.8 This took, 397.292, seconds. -------------------------------------------------- n (n x) This for the curve for the limit of the log of the coefficient of, t w , 1 divided by n, in the rational function, ------------- 3 -t w - t + 1 0.38 HHHHHHHHHHHHHH + HHHHH HHHHHH 0.36 HHHH HH + HHH HHH 0.34 HH HH + HHH HH + H H 0.32 HHH HH + HHH HH 0.3 H HH + HH H 0.28 HH H + H HH 0.26 HH H + HH H 0.24H H +H H 0.22 HH + H 0.2 H +-+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--*- 0.1 0.15 0.2 0.25 0.3 This took, 2.557, seconds. -------------------------------------------------- This is the generating function for monomer-dimer tilings of an n by 4 recta\ ngle n (n x) This for the curve for the limit of the log of the coefficient of, t w , 7 6 5 2 5 divided by n, in the rational function, - (t - 2 t w - 3 t w - 3 t w 4 2 5 4 3 2 4 3 2 2 3 + 3 t w - 5 t + 5 t w + 3 t w + 2 t + 11 t w - 3 t w + 6 t 2 2 / 8 2 7 3 6 4 9 - 9 t w - 3 t - 2 t w - 2 t + 1) / (-t w - 2 t w - t w + t / 8 7 2 5 4 8 7 6 2 5 3 4 4 + t w - 3 t w + 3 t w - t - 9 t w + 6 t w + 14 t w - 3 t w 7 6 5 2 4 3 3 4 6 5 4 2 - 9 t + 19 t w + 29 t w - 18 t w + t w + 5 t + 24 t w - 41 t w 3 3 5 4 3 2 2 3 4 3 + 4 t w + 21 t - 40 t w - 4 t w + 2 t w - 9 t - 27 t w 2 2 3 2 2 2 + 13 t w - 15 t + 21 t w + t w + 5 t + 5 t w + 3 t - 1) + HHHHHHHHHHHHHHHHHHHHHHH + HHHHHHHHH HH 2.4 HHHHHH + HHHHH + HHH + HHH 2.2 HHH + HH + HHH + HHH 2 + HH + HH + HH + HH + HH 1.8 HH + HH + HH + HH 1.6 HH +**+---+--+---+---+--+---+--+---+---+--+---+---+--+---+--+---+---+--+---+--- 0.2 0.4 0.6 0.8 This took, 2.070, seconds. --------------------------------------------------