A025603 Number of n-move queen paths on 8x8 board from given corner to any square.

1, 21, 465, 10565, 241697, 5539893, 127041105, 2913686981, 66827609633, 1532754884725, 35155272163473, 806321934125125, 18493816732267425, 424174583966543669, 9728877611505065297, 223141752041771533125, 5117984163043834408865, 117386198048567829057141

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..735

Formula

G.f.: -(3*x-1) *(16*x^3-4*x^2-5*x+1) *(112*x^4-124*x^3-8*x^2+11*x-1) / (112896*x^9 -170880*x^8 +29184*x^7 +55636*x^6 -26128*x^5 +79*x^4 +2120*x^3 -482*x^2 +40*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(add(b(n-1, i+t*r[1], j+t*r[2]), r=[[1, 1],
      [1, -1], [-1, 1], [-1, -1], [0, 1], [0, -1], [1, 0],
      [-1, 0]]), t=1..7)))
    end:
a:= n-> b(n, 7, 7):
seq(a(n), n=0..20);  # 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[Sum[b[n-1, i+t*r[[1]], j+t*r[[2]]], {r, {{1, 1}, {1, -1}, {-1, 1}, {-1, -1}, {0, 1}, {0, -1}, {1, 0}, {-1, 0}}}], {t, 1, 7}]]]; 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: A126996 A158603 A307600 * A296586 A269922 A006298

Adjacent sequences: A025600 A025601 A025602 * A025604 A025605 A025606

Keyword

nonn,easy

Author

David W. Wilson

Status

approved