A187290 - OEIS

%I #15 Apr 23 2018 02:58:50

%S 0,0,720,4576,13640,28224,48232,73408,103692,139056,179500,225024,

%T 275628,331312,392076,457920,528844,604848,685932,772096,863340,

%U 959664,1061068,1167552,1279116,1395760,1517484,1644288,1776172,1913136,2055180,2202304

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

%C Row 5 of A187286.

%H R. H. Hardin, <a href="/A187290/b187290.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 2540*n^2 - 12896*n + 14016 for n>7.

%F Conjectures from _Colin Barker_, Apr 22 2018: (Start)

%F G.f.: 4*x^3*(180 + 604*x + 518*x^2 + 78*x^3 - 24*x^4 - 64*x^5 - 15*x^6 - 7*x^7) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.

%F (End)

%e Some solutions for 4 X 4:

%e   0 5 1 0    0 0 2 1    5 0 0 0    3 0 4 5    0 0 1 0

%e   0 0 0 0    0 0 0 0    4 3 0 0    2 0 0 0    0 0 2 0

%e   0 4 2 3    5 4 3 0    0 0 0 0    0 0 0 0    5 4 3 0

%e   0 0 0 0    0 0 0 0    0 2 0 1    1 0 0 0    0 0 0 0

%Y Cf. A187286.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 08 2011