cp's OEIS Frontend

A187049 Number of 5-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.

%I A187049 #11 Apr 20 2018 10:05:11
%S A187049 0,0,8,456,2896,9216,20648,37472,59524,86656,118868,156160,198532,
%T A187049 245984,298516,356128,418820,486592,559444,637376,720388,808480,
%U A187049 901652,999904,1103236,1211648,1325140,1443712,1567364,1696096,1829908,1968800,2112772
%N A187049 Number of 5-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.
%C A187049 Row 5 of A187046.
%H A187049 R. H. Hardin, <a href="/A187049/b187049.txt">Table of n, a(n) for n = 1..35</a>
%F A187049 Empirical: a(n) = 2540*n^2 - 21128*n + 43936 for n>7.
%F A187049 Conjectures from _Colin Barker_, Apr 20 2018: (Start)
%F A187049 G.f.: 4*x^3*(2 + 108*x + 388*x^2 + 472*x^3 + 308*x^4 + 70*x^5 - 41*x^6 - 37*x^7) / (1 - x)^3.
%F A187049 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
%F A187049 (End)
%e A187049 Some solutions for 4 X 4:
%e A187049 ..0..0..0..0....0..0..0..0....0..0..3..0....4..0..0..0....0..5..0..1
%e A187049 ..0..0..1..0....0..4..0..0....0..2..0..4....0..5..0..1....0..0..0..0
%e A187049 ..0..4..0..2....3..0..1..0....0..0..0..0....0..0..3..0....0..2..0..4
%e A187049 ..5..0..3..0....0..2..0..5....0..5..0..1....0..2..0..0....0..0..3..0
%Y A187049 Cf. A187046.
%K A187049 nonn
%O A187049 1,3
%A A187049 _R. H. Hardin_, Mar 02 2011