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A350729 Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n king graph.

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%I A350729 #13 Feb 16 2025 08:34:02
%S A350729 1,1,1,1,12,1,1,48,48,1,1,208,392,208,1,1,768,4678,4678,768,1,1,2752,
%T A350729 43676,171592,43676,2752,1,1,9472,406396,4743130,4743130,406396,9472,
%U A350729 1,1,32000,3568906,132202038,364618672,132202038,3568906,32000,1
%N A350729 Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n king graph.
%H A350729 Andrew Howroyd, <a href="/A350729/b350729.txt">Table of n, a(n) for n = 1..231</a>
%H A350729 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>
%H A350729 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>
%F A350729 T(m,n) = T(n,m).
%e A350729 Array begins:
%e A350729 ===========================================================
%e A350729 m\n | 1    2      3         4           5             6 ...
%e A350729 ----+------------------------------------------------------
%e A350729   1 | 1    1      1         1           1             1 ...
%e A350729   2 | 1   12     48       208         768          2752 ...
%e A350729   3 | 1   48    392      4678       43676        406396 ...
%e A350729   4 | 1  208   4678    171592     4743130     132202038 ...
%e A350729   5 | 1  768  43676   4743130   364618672   28808442502 ...
%e A350729   6 | 1 2752 406396 132202038 28808442502 6544911081900 ...
%e A350729      ...
%Y A350729 Rows 1..5 are A000012, A339760, A339761, A339762, A339763.
%Y A350729 Main diagonal is A308129.
%Y A350729 Cf. A272445, A307026, A329118, A339098, A339190.
%K A350729 nonn,tabl
%O A350729 1,5
%A A350729 _Andrew Howroyd_, Jan 16 2022