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%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
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