A025606 Number of n-move queen paths on 8x8 board from given corner to adjacent corner.

0, 1, 8, 163, 3398, 76753, 1751700, 40139295, 920426818, 21110069229, 484177665424, 11105105040891, 254707005772222, 5841966668784265, 133991488702577676, 3073231857864304087, 70487714816049472186, 1616707794524130044965, 37080845818916250489864

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..736

Formula

G.f.: -(602112*x^12 -576768*x^11 -530368*x^10 +580832*x^9 +116752*x^8 -198176*x^7 +8788*x^6 +26462*x^5 -4839*x^4 -956*x^3 +354*x^2 -34*x+1) *(3*x-1)^2 *x / ((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) *(1152*x^7 -36*x^6 -816*x^5 +49*x^4 +152*x^3 -14*x^2 -8*x+1)). - Alois P. Heinz, Jun 28 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},
      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, 0, 7):
seq(a(n), n=0..20);  # Alois P. Heinz, Jun 28 2012

Mathematica

b[n_, i_, j_] := b[n, i, j] = If[n<0 || i<0 || i>7 || j<0 || j>7, 0, If[Union[{n, i, j}] == {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, 0, 7]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 28 2015, after Alois P. Heinz *)

Crossrefs

Sequence in context: A316998 A075387 A143857 * A224899 A281830 A299075

Adjacent sequences: A025603 A025604 A025605 * A025607 A025608 A025609

Keyword

nonn,easy

Author

David W. Wilson

Status

approved