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A187509 Number of 4-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

%I A187509 #16 Aug 23 2025 00:02:18
%S A187509 0,2,36,115,236,399,604,851,1140,1471,1844,2259,2716,3215,3756,4339,
%T A187509 4964,5631,6340,7091,7884,8719,9596,10515,11476,12479,13524,14611,
%U A187509 15740,16911,18124,19379,20676,22015,23396,24819,26284,27791,29340,30931,32564,34239
%N A187509 Number of 4-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.
%H A187509 R. H. Hardin, <a href="/A187509/b187509.txt">Table of n, a(n) for n = 1..50</a>
%F A187509 Empirical: a(n) = 21*n^2 - 68*n + 51 for n>2.
%F A187509 Empirical g.f.: x^2*(2+30*x+13*x^2-3*x^3)/(1-x)^3. - _Colin Barker_, Jan 22 2012
%e A187509 Some solutions for 4X4
%e A187509 ..0..0..0..0....0..0..0..0....0..4..2..0....0..4..0..0....0..0..0..0
%e A187509 ..1..2..3..0....0..1..0..0....0..0..3..1....0..2..3..0....0..1..2..0
%e A187509 ..0..0..4..0....0..2..3..0....0..0..0..0....0..0..1..0....0..0..3..4
%e A187509 ..0..0..0..0....0..0..4..0....0..0..0..0....0..0..0..0....0..0..0..0
%Y A187509 Row 4 of A187507.
%K A187509 nonn
%O A187509 1,2
%A A187509 _R. H. Hardin_, Mar 10 2011