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%I #7 Dec 20 2024 10:45:03
%S 1,1,1,1,2,1,1,3,3,1,1,4,8,4,1,1,5,17,17,5,1,1,6,38,52,38,6,1,1,7,78,
%T 160,160,78,7,1,1,8,164,469,824,469,164,8,1,1,9,332,1337,3501,3501,
%U 1337,332,9,1,1,10,680,3750,16262,22144,16262,3750,680,10,1
%N Array read by antidiagonals: T(m,n) is the number of Hamiltonian paths in an m X n grid which start in the top left corner.
%C These paths are also called Greek-key tours. The path can end anywhere.
%H Andrew Howroyd, <a href="/A378938/b378938.txt">Table of n, a(n) for n = 1..435</a> (first 29 antidiagonals)
%F T(m,n) = T(n,m).
%e Array begins:
%e ======================================================
%e m\n | 1 2 3 4 5 6 7 8 ...
%e ----+-------------------------------------------------
%e 1 | 1 1 1 1 1 1 1 1 ...
%e 2 | 1 2 3 4 5 6 7 8 ...
%e 3 | 1 3 8 17 38 78 164 332 ...
%e 4 | 1 4 17 52 160 469 1337 3750 ...
%e 5 | 1 5 38 160 824 3501 16262 68591 ...
%e 6 | 1 6 78 469 3501 22144 144476 899432 ...
%e 7 | 1 7 164 1337 16262 144476 1510446 13506023 ...
%e 8 | 1 8 332 3750 68591 899432 13506023 180160012 ...
%e ...
%Y Main diagonal is A145157.
%Y Rows 1..8 are A000012, A000027, A046994, A046995, A145156, A160240, A160241, A374307.
%Y Cf. A332307, A064298, A271465, A271592, A288518.
%K nonn,tabl
%O 1,5
%A _Andrew Howroyd_, Dec 20 2024