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Number of (undirected) Hamiltonian paths on the n X n king graph.
5

%I #9 Feb 16 2025 08:33:55

%S 1,12,392,171592,364618672,6544911081900,829555065360355292,

%T 817534730458899350635436,6154392250018061759082363305112,

%U 360916610325065945171647827293872547848,165298493343313203241690299664254975948394404072

%N Number of (undirected) Hamiltonian paths on the n X n king graph.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>

%F a(n) = A158651(n)/2 for n > 1.

%Y Main diagonal of A350729.

%Y Cf. A140518, A158651, A272445, A288033.

%K nonn,hard,changed

%O 1,2

%A _Eric W. Weisstein_, May 14 2019

%E a(1) corrected by _Andrew Howroyd_, Jan 16 2022