cp's OEIS Frontend

A186857 Number of 8-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

%I A186857 #14 Jan 02 2023 21:56:31
%S A186857 16,2208,57392,405040,1508784,3846192,7777808,13502064,21089312,
%T A186857 30521216,41748432,54726992,69434272,85865344,104020208,123898864,
%U A186857 145501312,168827552,193877584,220651408,249149024,279370432,311315632,344984624,380377408,417493984
%N A186857 Number of 8-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.
%H A186857 Andrew Howroyd, <a href="/A186857/b186857.txt">Table of n, a(n) for n = 1..1000</a>
%F A186857 a(n) = 861896*n^2 - 6840120*n + 12695408 for n >= 12. - _Andrew Howroyd_, Jan 02 2023
%e A186857 Some solutions for 5 X 5:
%e A186857   0 0 0 0 0     0 3 8 0 0     0 0 0 4 7     3 0 5 0 0
%e A186857   0 0 7 0 0     0 0 0 0 0     2 5 8 0 0     6 0 2 0 0
%e A186857   0 0 2 5 0     2 0 4 7 0     0 0 3 6 0     0 4 7 0 1
%e A186857   3 6 0 8 0     0 6 0 0 0     0 1 0 0 0     0 0 0 0 0
%e A186857   0 1 4 0 0     0 1 0 5 0     0 0 0 0 0     0 8 0 0 0
%o A186857 (PARI) row(8, 30) \\ row(m,n) defined in A186851. - _Andrew Howroyd_, Jan 02 2023
%Y A186857 Row 8 of A186851.
%K A186857 nonn
%O A186857 1,1
%A A186857 _R. H. Hardin_, Feb 27 2011
%E A186857 Terms a(8) and beyond from _Andrew Howroyd_, Jan 02 2023