A025599 Number of n-move knight paths on 8 X 8 board from given corner to any square.

1, 2, 12, 64, 404, 2352, 14396, 85608, 517796, 3100928, 18678652, 112130536, 674473028, 4052292096, 24363059260, 146416625608, 880136072420, 5289934135040, 31796930379452, 191117281480168, 1148752620931652, 6904721644495296, 41502080416224764

Offset

0,2

Links

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

Formula

G.f.: -(72*x^7+128*x^6-42*x^5-108*x^4-3*x^3+21*x^2+x-1) / (96*x^8 -16*x^7 -276*x^6 -42*x^5 +162*x^4 +29*x^3 -27*x^2 -3*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=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, 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[n == 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, 7, 7]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 28 2015, after Alois P. Heinz *)

Crossrefs

Sequence in context: A052896 A215128 A190155 * A162973 A321989 A226226

Adjacent sequences: A025596 A025597 A025598 * A025600 A025601 A025602

Keyword

nonn

Author

David W. Wilson

Status

approved