cp's OEIS Frontend

A187378 Number of 4-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

%I A187378 #18 Aug 22 2025 05:57:12
%S A187378 0,4,40,132,278,478,732,1040,1402,1818,2288,2812,3390,4022,4708,5448,
%T A187378 6242,7090,7992,8948,9958,11022,12140,13312,14538,15818,17152,18540,
%U A187378 19982,21478,23028,24632,26290,28002,29768,31588,33462,35390,37372,39408,41498,43642
%N A187378 Number of 4-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
%H A187378 R. H. Hardin, <a href="/A187378/b187378.txt">Table of n, a(n) for n = 1..50</a>
%F A187378 Empirical: a(n) = 27*n^2 - 97*n + 88 for n>2.
%F A187378 Empirical g.f.: 2*x^2*(2+14*x+12*x^2-x^3)/(1-x)^3. - _Colin Barker_, Jan 22 2012
%e A187378 Some solutions for 4X4
%e A187378 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..2....4..0..0..0
%e A187378 ..3..0..0..0....0..0..2..0....0..0..0..0....0..0..1..3....0..3..0..0
%e A187378 ..4..2..0..0....0..0..3..1....3..1..0..0....0..0..0..4....0..0..2..0
%e A187378 ..0..0..1..0....0..0..4..0....4..2..0..0....0..0..0..0....0..0..0..1
%Y A187378 Row 4 of A187377.
%K A187378 nonn
%O A187378 1,2
%A A187378 _R. H. Hardin_, Mar 09 2011