A333863 - OEIS

%I #27 Jun 29 2023 11:01:14

%S 1,16,117204,440051896440,825830699757513748579,

%T 769203260676279544212492116449800,

%U 354179806054404909542325896762875458037457353029,80433401895946253522491939742836167238530417144721958187080077425

%N Number of Hamiltonian paths in a 2*(2*n+1) X (2*n+1) grid starting at the upper left corner and finishing in the lower right corner.

%H Ed Wynn, <a href="/A333863/b333863.txt">Table of n, a(n) for n = 0..9</a>

%F a(n) = A333580(2*(2*n+1), 2*n+1).

%o (Python)

%o # Using graphillion

%o from graphillion import GraphSet

%o import graphillion.tutorial as tl

%o def A333863(n):

%o     universe = tl.grid(4 * n + 1, 2 * n)

%o     GraphSet.set_universe(universe)

%o     start, goal = 1, 2 * (2 * n + 1) ** 2

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

%o     return paths.len()

%o print([A333863(n) for n in range(7)])

%Y Cf. A001184, A333580, A333585, A333864.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 08 2020

%E More terms from _Ed Wynn_, Jun 28 2023