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A025594 Number of n-move bishop paths on 8x8 board from given corner to opposite corner. 1

%I

%S 0,1,6,43,324,2565,21202,181071,1583440,14074121,126458750,1144310003,

%T 10401799580,94825890253,866041203690,7918632503383,72456324725928,

%U 663284620905297,6073618350612502,55625356328239995,509503126813055092,4667146731457616789

%N Number of n-move bishop paths on 8x8 board from given corner to opposite corner.

%H Alois P. Heinz, <a href="/A025594/b025594.txt">Table of n, a(n) for n = 0..320</a>

%F G.f.: -(32*x^6 +56*x^5 -214*x^4 -17*x^3 +61*x^2 -15*x+1) *x / ((x+1) *(192*x^7 +184*x^6-1066*x^5 -113*x^4+468*x^3 -166*x^2+22*x-1)). - _Alois P. Heinz_, Jun 26 2012

%p b:= proc(n, i, j) option remember;

%p `if`(n<0 or i<0 or i>7 or j<0 or j>7, 0, `if`({n, i, j}={0},

%p 1, add (add (b(n-1, i+t*r[1], j+t*r[2]), r=[[1, 1], [1, -1],

%p [-1, 1], [-1, -1]]), t=1..7)))

%p end:

%p a:= n-> b (n, 7, 7):

%p seq (a(n), n=0..30); # _Alois P. Heinz_, Jun 26 2012

%t b[n_, i_, j_] := b[n, i, j] = If[n<0 || i<0 || i>7 || j<0 || j>7, 0, If[Union[{n, i, j}] == {0}, 1, Sum[Sum[b[n-1, i + t*r[[1]], j + t*r[[2]]], {r, {{1, 1}, {1, -1}, {-1, 1}, {-1, -1}}}], {t, 1, 7}]]]; a[n_] := b[n, 7, 7]; Table[a[n], {n, 0, 30}] (* _Jean-Fran├žois Alcover_, May 28 2015, after _Alois P. Heinz_ *)

%K nonn

%O 0,3

%A _David W. Wilson_

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Last modified May 25 00:03 EDT 2022. Contains 354047 sequences. (Running on oeis4.)