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A025599 Number of n-move knight paths on 8 X 8 board from given corner to any square. 1
1, 2, 12, 64, 404, 2352, 14396, 85608, 517796, 3100928, 18678652, 112130536, 674473028, 4052292096, 24363059260, 146416625608, 880136072420, 5289934135040, 31796930379452, 191117281480168, 1148752620931652, 6904721644495296, 41502080416224764 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified May 29 05:00 EDT 2022. Contains 354122 sequences. (Running on oeis4.)