A333689 - OEIS

%I #12 Apr 02 2020 14:05:54

%S 1,101,7056,610765,53968755,4775133828,422813081886,37441305792927,

%T 3315577406171322,293609559097456363,26000534802119070508,

%U 2302473191851860468948,203895143590466986654399,18055900558029962460378646,1598937211532791928425001493,141593611215040047912334138664

%N Number of self-avoiding paths in (2*n+1) X 5 grid starting the upper left corner, passing through the center of grid and finishing the lower right corner.

%H Seiichi Manyama, <a href="/A333689/b333689.txt">Table of n, a(n) for n = 0..500</a>

%o (Python)

%o # Using graphillion

%o from graphillion import GraphSet

%o import graphillion.tutorial as tl

%o def A333685(n, k):

%o     if n == 0 or k == 0: return 1

%o     universe = tl.grid(2 * n, 2 * k)

%o     GraphSet.set_universe(universe)

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

%o     paths = GraphSet.paths(start, goal).including((start + goal) // 2)

%o     return paths.len()

%o def A333689(n):

%o     return A333685(n, 2)

%o print([A333689(n) for n in range(15)])

%Y Column 2 of A333685.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 02 2020