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A186853 Number of 4-step knight's tours on an (n+2) X (n+2) board summed over all starting positions. 2

%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

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)