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A025595 Number of n-move king paths on 8x8 board from given corner to any square. 1
1, 3, 18, 105, 684, 4550, 31340, 219555, 1559835, 11177190, 80573373, 583082082, 4230475092, 30745373256, 223692489189, 1628685532071, 11863934648190, 86447927584521, 630040117048380, 4592393936655066, 33477073967039868, 244050825770095095, 1779217416632500479 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

A. Bostan, Computer Algebra for Lattice Path Combinatorics, Seminaire de Combinatoire Ph. Flajolet, March 28 2013.

FORMULA

G.f.: -(48*x^9 +120*x^8 -126*x^7 -457*x^6 -175*x^5 +162*x^4 +75*x^3 -18*x^2 -6*x+1) / ((3*x-1) *(3*x^3-3*x-1) *(3*x^3-9*x^2-3*x+1) *(3*x^3+9*x^2+6*x-1)). - Alois P. Heinz, Jun 25 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, 1], [1, 0], [1, -1],

          [0, 1], [0, -1], [-1, 1], [-1, 0], [-1, -1]])))

    end:

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

seq(a(n), n=0..30);  # Alois P. Heinz, Jun 25 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, 1}, {1, 0}, {1, -1}, {0, 1}, {0, -1}, {-1, 1}, {-1, 0}, {-1, -1}}}]]]; 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: A136779 A106328 A007277 * A151331 A137962 A267662

Adjacent sequences:  A025592 A025593 A025594 * A025596 A025597 A025598

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified December 2 17:59 EST 2021. Contains 349445 sequences. (Running on oeis4.)