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A025602 Number of n-move knight paths on 8x8 board from given corner to adjacent corner. 1
0, 0, 0, 0, 0, 18, 0, 852, 0, 32974, 0, 1216736, 0, 44265306, 0, 1602980908, 0, 57958913510, 0, 2094514154552, 0, 75677759126258, 0, 2734176449182980, 0, 98781516222538110, 0, 3568795954184265360, 0, 128933769847371450506, 0, 4658126510414596025052, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

FORMULA

From Vaclav Kotesovec, Nov 26 2012: (Start)

G.f.: -(2*x^5*(-9 + 186*x^2 - 1433*x^4 + 5172*x^6 - 9228*x^8 + 8048*x^10 - 3360*x^12 + 768*x^14))/((-1+x)*(1+x)*(-1+2*x)*(1+2*x)*(1 - 3*x - 27*x^2 + 29*x^3 + 162*x^4 - 42*x^5 - 276*x^6 - 16*x^7 + 96*x^8)*(1 + 3*x - 27*x^2 - 29*x^3 + 162*x^4 + 42*x^5 - 276*x^6 + 16*x^7 + 96*x^8))

Nonzero terms a(n+2)/a(n) tends to 36.12804064450295915...

(End)

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

      [-1, -2], [2, 1], [2, -1], [-2, 1], [-2, -1]])))

    end:

a:= n-> b(n, 0, 7):

seq(a(n), n=0..40);  # Alois P. Heinz, Jun 28 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[b[n-1, i+r[[1]], j+r[[2]]], {r, {{1, 2}, {1, -2}, {-1, 2}, {-1, -2}, {2, 1}, {2, -1}, {-2, 1}, {-2, -1}}}]]]; a[n_] := b[n, 0, 7]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, May 28 2015, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A231962 A052441 A221394 * A088126 A040327 A040328

Adjacent sequences:  A025599 A025600 A025601 * A025603 A025604 A025605

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified November 22 13:47 EST 2019. Contains 329393 sequences. (Running on oeis4.)