Number of perfect matchings in the graph C_{2n} X C_k
kが3以上のとき、計算してみた。
a341533(n, k) = round(sqrt(prod(a=1, n, prod(b=1, k, 4*sin((2*a-1)*Pi/(2*n))^2+4*sin((2*b-1)*Pi/k)^2))));
a341738(n, k) = round(sqrt(prod(a=1, n, prod(b=1, k-1, 4*sin((2*a-1)*Pi/(2*n))^2+4*sin(2*b*Pi/k)^2))));
a341739(n, k) = round( prod(a=1, n-1, prod(b=1, k, 4*sin(a*Pi/n)^2 +4*sin((2*b-1)*Pi/(2*k))^2)));
T(n, k) = a341533(n, k)/2+a341738(n, k)+2*((k+1)%2)*a341739(n, ceil(k/2));
K=7;
for(n=2, 10, for(k=3, K, print1(T(n, k), ", ")); print)
出力結果
50, 272, 722, 3108, 10082,
224, 3108, 9922, 90176, 401998,
1058, 39952, 155682, 3113860, 19681538,
5054, 537636, 2540032, 114557000, 1034315998,
24200, 7379216, 41934482, 4357599552, 55820091938,
115934, 102144036, 694861522, 169094614280, 3044533460992,
555458, 1418981392, 11527389122, 6640849944580, 166779871224962,
2661344, 19742287908, 191304901282, 262671237617216, 9152970837103102,
12751250, 274848860432, 3175220160032, 10433179552323108, 502711247500143362,
