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 A187156 Number of 3-step one space at a time bishop's tours on an n X n board summed over all starting positions. 2

%I

%S 0,0,20,64,132,224,340,480,644,832,1044,1280,1540,1824,2132,2464,2820,

%T 3200,3604,4032,4484,4960,5460,5984,6532,7104,7700,8320,8964,9632,

%U 10324,11040,11780,12544,13332,14144,14980,15840,16724,17632,18564,19520,20500

%N Number of 3-step one space at a time bishop's tours on an n X n board summed over all starting positions.

%C Row 3 of A187155.

%H R. H. Hardin, <a href="/A187156/b187156.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 12*n^2 - 40*n + 32 for n>1.

%F Conjectures from _Colin Barker_, Feb 28 2018: (Start)

%F G.f.: 4*x^3*(5 + x) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

%F (End)

%e Some solutions for 4 X 4:

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

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

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

%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....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 November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)