A338297 - OEIS

%I #44 Jan 12 2021 02:50:43

%S 6,228,4800,76116,1094316,14557092,183735204,2230289220,26275912776,

%T 302338568832,3412921463352,37923555328200,415863933818988,

%U 4509400849281240,48428461587426108,515767225814395500,5452991323044249720,57282647077608267072,598324561437126968664,6217929367753246782612

%N Number of Hamiltonian paths in C_6 X P_n.

%H Seiichi Manyama, <a href="/A338297/b338297.txt">Table of n, a(n) for n = 1..25</a>

%o (Python)

%o # Using graphillion

%o from graphillion import GraphSet

%o def make_CnXPk(n, k):

%o     grids = []

%o     for i in range(1, k + 1):

%o         for j in range(1, n):

%o             grids.append((i + (j - 1) * k, i + j * k))

%o         grids.append((i + (n - 1) * k, i))

%o     for i in range(1, k * n, k):

%o         for j in range(1, k):

%o             grids.append((i + j - 1, i + j))

%o     return grids

%o def A(start, goal, n, k):

%o     universe = make_CnXPk(n, k)

%o     GraphSet.set_universe(universe)

%o     paths = GraphSet.paths(start, goal, is_hamilton=True)

%o     return paths.len()

%o def B(n, k):

%o     m = k * n

%o     s = 0

%o     for i in range(1, m):

%o         for j in range(i + 1, m + 1):

%o             s += A(i, j, n, k)

%o     return s

%o def A338297(n):

%o     return B(6, n)

%o print([A338297(n) for n in range(1, 11)])

%Y Cf. A003689 (C_3 X P_n), A003752 (C_4 X P_n), A003732 (C_5 X P_n), A268894 (C_n X P_n).

%Y Cf. A180582, A339143, A338962.

%K nonn

%O 1,1

%A _Seiichi Manyama_, Dec 18 2020