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A187157 Number of 4-step one space at a time bishop's tours on an n X n board summed over all starting positions. 1

%I

%S 0,0,8,92,248,476,776,1148,1592,2108,2696,3356,4088,4892,5768,6716,

%T 7736,8828,9992,11228,12536,13916,15368,16892,18488,20156,21896,23708,

%U 25592,27548,29576,31676,33848,36092,38408,40796,43256,45788,48392,51068,53816

%N Number of 4-step one space at a time bishop's tours on an n X n board summed over all starting positions.

%C Row 4 of A187155.

%H R. H. Hardin, <a href="/A187157/b187157.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 36*n^2 - 168*n + 188 for n>2.

%F Conjectures from _Colin Barker_, Apr 20 2018: (Start)

%F G.f.: 4*x^3*(2 + 17*x - x^2) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.

%F (End)

%e Some solutions for 4 X 4:

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

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

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

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

%Y Cf. A187155.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 06 2011

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Last modified September 24 17:17 EDT 2021. Contains 347651 sequences. (Running on oeis4.)