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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 1

%I

%S 0,2,36,115,236,399,604,851,1140,1471,1844,2259,2716,3215,3756,4339,

%T 4964,5631,6340,7091,7884,8719,9596,10515,11476,12479,13524,14611,

%U 15740,16911,18124,19379,20676,22015,23396,24819,26284,27791,29340,30931,32564,34239

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

%C Row 4 of A187507

%H R. H. Hardin, <a href="/A187509/b187509.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 21*n^2 - 68*n + 51 for n>2.

%F Empirical G.f.: x^2*(2+30*x+13*x^2-3*x^3)/(1-x)^3. [Colin Barker, Jan 22 2012]

%e Some solutions for 4X4

%e ..0..0..0..0....0..0..0..0....0..4..2..0....0..4..0..0....0..0..0..0

%e ..1..2..3..0....0..1..0..0....0..0..3..1....0..2..3..0....0..1..2..0

%e ..0..0..4..0....0..2..3..0....0..0..0..0....0..0..1..0....0..0..3..4

%e ..0..0..0..0....0..0..4..0....0..0..0..0....0..0..0..0....0..0..0..0

%K nonn

%O 1,2

%A _R. H. Hardin_ Mar 10 2011

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Last modified January 18 01:10 EST 2022. Contains 350410 sequences. (Running on oeis4.)