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%I #14 Mar 28 2020 10:11:36
%S 1,0,1,0,1,1,0,1,0,1,0,1,2,1,1,0,1,0,4,0,1,0,1,4,8,8,1,1,0,1,0,23,0,
%T 16,0,1,0,1,8,55,86,47,32,1,1,0,1,0,144,0,397,0,64,0,1,0,1,16,360,948,
%U 1770,1584,264,128,1,1,0,1,0,921,0,11658,0,6820,0,256,0,1
%N Array read by antidiagonals: T(n,m) = number of directed Hamiltonian walks from NW to SW corners on a grid with n rows and m columns.
%H Andrew Howroyd, <a href="/A271592/b271592.txt">Antidiagonals n = 1..27, flattened</a>
%F T(n,m)=0 for n odd and m even, T(1,n)=0 for n>1.
%F T(2,n)=T(n,1)=T(2*n,2)=1, T(3,2*n+1)=T(n+1,3)=2^n.
%e The start of the sequence as table:
%e * 1 0 0 0 0 0 0 0 0 ...
%e * 1 1 1 1 1 1 1 1 1 ...
%e * 1 0 2 0 4 0 8 0 16 ...
%e * 1 1 4 8 23 55 144 360 921 ...
%e * 1 0 8 0 86 0 948 0 10444 ...
%e * 1 1 16 47 397 1770 11658 59946 359962 ...
%e * 1 0 32 0 1584 0 88418 0 4999752 ...
%e * 1 1 64 264 6820 52387 909009 8934966 130373192 ...
%e * 1 0 128 0 28002 0 7503654 0 2087813834 ...
%e * ...
%o (Python)
%o # Using graphillion
%o from graphillion import GraphSet
%o import graphillion.tutorial as tl
%o def A271592(n, k):
%o if k == 1: return 1
%o universe = tl.grid(k - 1, n - 1)
%o GraphSet.set_universe(universe)
%o start, goal = 1, n
%o paths = GraphSet.paths(start, goal, is_hamilton=True)
%o return paths.len()
%o print([A271592(j + 1, i - j + 1) for i in range(12) for j in range(i + 1)]) # _Seiichi Manyama_, Mar 28 2020
%Y Column 4 is aerated A014524, column 5 is A014585.
%Y Rows include A181688, A181689.
%Y Main diagonal is A000532.
%Y Cf. A333580.
%K nonn,tabl
%O 1,13
%A _Andrew Howroyd_, Apr 10 2016
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