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A306282 Triangle read by rows: T(n,k) is the number of (directed) Hamiltonian paths in the n X k knight graph.

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%I A306282 #11 Feb 16 2025 08:33:55
%S A306282 1,0,0,0,0,0,0,0,16,0,0,0,0,164,1728,0,0,0,1488,37568,6637920,0,0,104,
%T A306282 12756,1245736,779938932,165575218320,0,0,792,62176,36122108
%N A306282 Triangle read by rows: T(n,k) is the number of (directed) Hamiltonian paths in the n X k knight graph.
%H A306282 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>
%H A306282 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnightGraph.html">Knight Graph</a>
%e A306282 Triangle begins:
%e A306282 n\k | 1  2    3      4        5          6             7
%e A306282 ----+----------------------------------------------------
%e A306282 1   | 1;
%e A306282 2   | 0, 0;
%e A306282 3   | 0, 0,   0;
%e A306282 4   | 0, 0,  16,     0;
%e A306282 5   | 0, 0,   0,   164,    1728;
%e A306282 6   | 0, 0,   0,  1488,   37568,   6637920;
%e A306282 7   | 0, 0, 104, 12756, 1245736, 779938932, 165575218320;
%Y A306282 T(n,n) gives A165134.
%Y A306282 Cf. A118067, A123935.
%K A306282 nonn,tabl,more
%O A306282 1,9
%A A306282 _Seiichi Manyama_, Feb 03 2019