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A188779 Number of 4-turn bishop's tours on an n X n board summed over all starting positions 1

%I #11 Apr 04 2016 16:14:07

%S 0,0,24,328,1720,5816,15424,34736,69776,128528,221448,361528,564872,

%T 850696,1241968,1765344,2451872,3336864,4460664,5868456,7611096,

%U 9744856,12332320,15442064,19149616,23537072,28694120,34717592,41712552,49791784

%N Number of 4-turn bishop's tours on an n X n board summed over all starting positions

%C Row 4 of A188777

%H R. H. Hardin, <a href="/A188779/b188779.txt">Table of n, a(n) for n = 1..42</a>

%F Empirical: a(n) = 4*a(n-1) -4*a(n-2) -4*a(n-3) +10*a(n-4) -4*a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8)

%F Contribution from _Vaclav Kotesovec_, Sep 01 2012: (Start)

%F Empirical: G.f.: 8*x^3*(3 + 29*x + 63*x^2 + 43*x^3 + 14*x^4)/((1-x)^6*(1+x)^2)

%F Empirical: a(n) = -2 + 257*n/15 - 109*n^2/3 + 106*n^3/3 - 47*n^4/3 + 38*n^5/15 + (-1)^n*(2-n)

%F (End)

%e Some solutions for 4X4

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

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

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

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

%K nonn

%O 1,3

%A _R. H. Hardin_ Apr 10 2011

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Last modified March 29 20:15 EDT 2024. Contains 371281 sequences. (Running on oeis4.)