A025598 Number of n-move king paths on 8 X 8 board from given corner to adjacent corner.

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

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-François Alcover, May 28 2015, after Alois P. Heinz *)

Crossrefs

Sequence in context: A371337 A258012 A258002 * A115153 A172408 A204216

Adjacent sequences: A025595 A025596 A025597 * A025599 A025600 A025601

Keyword

nonn,easy

Author

David W. Wilson

Status

approved