cp's OEIS Frontend

A187510 Number of 5-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

%I A187510 #16 Aug 23 2025 00:01:44
%S A187510 0,0,40,184,435,788,1243,1800,2459,3220,4083,5048,6115,7284,8555,9928,
%T A187510 11403,12980,14659,16440,18323,20308,22395,24584,26875,29268,31763,
%U A187510 34360,37059,39860,42763,45768,48875,52084,55395,58808,62323,65940,69659,73480
%N A187510 Number of 5-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.
%H A187510 R. H. Hardin, <a href="/A187510/b187510.txt">Table of n, a(n) for n = 1..50</a>
%F A187510 Empirical: a(n) = 51*n^2 - 208*n + 200 for n>3.
%F A187510 Empirical g.f.: x^3*(40+64*x+3*x^2-5*x^3)/(1-x)^3. - _Colin Barker_, Jan 22 2012
%e A187510 Some solutions for 4X4
%e A187510 ..0..0..0..0....0..0..0..0....0..0..0..0....4..0..0..0....0..1..0..0
%e A187510 ..0..0..0..0....0..0..0..0....4..5..0..0....5..3..1..0....0..2..0..0
%e A187510 ..0..5..3..1....0..0..4..5....2..3..0..0....0..0..2..0....0..3..4..5
%e A187510 ..0..0..4..2....0..1..2..3....0..1..0..0....0..0..0..0....0..0..0..0
%Y A187510 Row 5 of A187507.
%K A187510 nonn
%O A187510 1,3
%A A187510 _R. H. Hardin_, Mar 10 2011