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

0, 1, 6, 43, 324, 2565, 21202, 181071, 1583440, 14074121, 126458750, 1144310003, 10401799580, 94825890253, 866041203690, 7918632503383, 72456324725928, 663284620905297, 6073618350612502, 55625356328239995, 509503126813055092, 4667146731457616789

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: A091129 A091128 A349302 * A098665 A153397 A005786

Adjacent sequences: A025591 A025592 A025593 * A025595 A025596 A025597

Keyword

nonn

Author

David W. Wilson

Status

approved