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%I #13 Jan 07 2023 20:10:47
%S 16,208,976,2576,5056,8320,12368,17200,22816,29216,36400,44368,53120,
%T 62656,72976,84080,95968,108640,122096,136336,151360,167168,183760,
%U 201136,219296,238240,257968,278480,299776,321856,344720,368368,392800
%N Number of 4-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.
%H Andrew Howroyd, <a href="/A186853/b186853.txt">Table of n, a(n) for n = 1..1000</a>
%F Empirical: a(n) = 392*n^2 - 1048*n + 496 for n > 3.
%F The above empirical formula is correct. See A186851 for details. - _Andrew Howroyd_, Jan 07 2023
%e Some solutions for 5 X 5:
%e 0 1 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 1 0 0
%e 0 0 3 0 0 0 0 0 0 0 0 0 0 0 1 4 0 0 0 2
%e 2 0 0 0 4 4 0 2 0 0 4 0 0 0 0 0 0 3 0 0
%e 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0
%e 0 0 0 0 0 0 0 0 1 0 0 3 0 0 0 0 0 0 0 0
%o (PARI) row(4, 30) \\ row(m, n) defined in A186851. - _Andrew Howroyd_, Jan 07 2023
%Y Row 4 of A186851.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 27 2011