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A025598 Number of n-move king paths on 8 X 8 board from given corner to adjacent corner. 1
0, 0, 0, 0, 0, 0, 0, 127, 1568, 17221, 157710, 1360107, 11104632, 87999275, 681209386, 5192306420, 39117179936, 292250754994, 2169869100416, 16036792568508, 118115950230120, 867736883991669, 6362604049648708, 46586411156710601, 340735507632772936 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

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

FORMULA

G.f.: -(267*x^9 +2097*x^8 +4104*x^7 -1898*x^6 -8970*x^5 -2100*x^4 +4314*x^3 +1932*x^2 -171*x-127) *x^7 / ((3*x-1) *(x+1) *(17*x^3+6*x^2-3*x-1) *(3*x^3+9*x^2+6*x-1) *(3*x^3-9*x^2-3*x+1) *(3*x^3-3*x-1) *(x^3+3*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, i, j]=[0, 0, 7],

       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, 7, 7):

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, i, j} == {0, 0, 7}, 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, 7, 7]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, May 28 2015, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A287653 A258012 A258002 * A115153 A172408 A204216

Adjacent sequences:  A025595 A025596 A025597 * A025599 A025600 A025601

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified January 23 13:57 EST 2022. Contains 350511 sequences. (Running on oeis4.)