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A025606 Number of n-move queen paths on 8x8 board from given corner to adjacent corner. 1
0, 1, 8, 163, 3398, 76753, 1751700, 40139295, 920426818, 21110069229, 484177665424, 11105105040891, 254707005772222, 5841966668784265, 133991488702577676, 3073231857864304087, 70487714816049472186, 1616707794524130044965, 37080845818916250489864 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified June 27 19:31 EDT 2022. Contains 354898 sequences. (Running on oeis4.)