login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Number of 7-step one space at a time bishop's tours on an n X n board summed over all starting positions.
1

%I #10 Apr 20 2018 10:05:22

%S 0,0,0,16,544,2328,6172,11576,18540,27064,37148,48792,61996,76760,

%T 93084,110968,130412,151416,173980,198104,223788,251032,279836,310200,

%U 342124,375608,410652,447256,485420,525144,566428,609272,653676,699640,747164

%N Number of 7-step one space at a time bishop's tours on an n X n board summed over all starting positions.

%C Row 7 of A187155.

%H R. H. Hardin, <a href="/A187160/b187160.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 780*n^2 - 6296*n + 12024 for n>5.

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

%F G.f.: 4*x^4*(4 + 124*x + 186*x^2 + 201*x^3 - 125*x^4) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

%F (End)

%e Some solutions for 4 X 4:

%e ..0..0..4..0....0..7..0..1....7..0..5..0....0..2..0..0....0..0..6..0

%e ..0..3..0..5....6..0..2..0....0..6..0..4....1..0..3..0....0..5..0..7

%e ..2..0..6..0....0..5..0..3....1..0..3..0....0..6..0..4....4..0..2..0

%e ..0..1..0..7....0..0..4..0....0..2..0..0....7..0..5..0....0..3..0..1

%Y Cf. A187155.

%K nonn

%O 1,4

%A _R. H. Hardin_, Mar 06 2011