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A025593 Number of n-move bishop paths on 8x8 board from given corner to same corner. 1
1, 0, 7, 42, 325, 2564, 21203, 181070, 1583441, 14074120, 126458751, 1144310002, 10401799581, 94825890252, 866041203691, 7918632503382, 72456324725929, 663284620905296, 6073618350612503, 55625356328239994, 509503126813055093, 4667146731457616788 (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.: (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-Fran├žois Alcover, May 28 2015, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A278152 A271427 A073506 * A218124 A048862 A208943

Adjacent sequences:  A025590 A025591 A025592 * A025594 A025595 A025596

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified February 19 12:48 EST 2018. Contains 299333 sequences. (Running on oeis4.)