A025593 Number of n-move bishop paths on 8x8 board from given corner to same corner.

1, 0, 7, 42, 325, 2564, 21203, 181070, 1583441, 14074120, 126458751, 1144310002, 10401799581, 94825890252, 866041203691, 7918632503382, 72456324725929, 663284620905296, 6073618350612503, 55625356328239994, 509503126813055093, 4667146731457616788

Offset

0,3

Links

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

Formula

G.f.: (5*x-1)*(32*x^6+32*x^5-164*x^4-52*x^3+71*x^2-16*x+1) / ((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, 0, 0):
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, 0, 0]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 28 2015, after Alois P. Heinz *)

Crossrefs

Sequence in context: A332082 A271427 A073506 * A218124 A048862 A208943

Adjacent sequences: A025590 A025591 A025592 * A025594 A025595 A025596

Keyword

nonn

Author

David W. Wilson

Status

approved