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A025594 Number of n-move bishop paths on 8x8 board from given corner to opposite corner. 1
0, 1, 6, 43, 324, 2565, 21202, 181071, 1583440, 14074121, 126458750, 1144310003, 10401799580, 94825890253, 866041203690, 7918632503383, 72456324725928, 663284620905297, 6073618350612502, 55625356328239995, 509503126813055092, 4667146731457616789 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..320

FORMULA

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

MAPLE

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

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

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

      [-1, 1], [-1, -1]]), t=1..7)))

    end:

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

seq (a(n), n=0..30);  # Alois P. Heinz, Jun 26 2012

MATHEMATICA

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-François Alcover, May 28 2015, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A015552 A091129 A091128 * A098665 A153397 A005786

Adjacent sequences:  A025591 A025592 A025593 * A025595 A025596 A025597

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified July 2 16:02 EDT 2020. Contains 335404 sequences. (Running on oeis4.)