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A025604 Number of n-move queen paths on 8x8 board from given corner to same corner. 1
1, 0, 21, 180, 3699, 78186, 1763689, 40219584, 921030783, 21114454518, 484210273013, 11105346505100, 254708804007115, 5841980066693506, 133991588716915713, 3073232605116594392, 70487720404861582487, 1616707836356340649102, 37080846132267449237645 (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

From Vaclav Kotesovec, Nov 26 2012: (Start)

G.f.: ((-1+3*x)*(-1 + 65*x - 1704*x^2 + 23568*x^3 - 178704*x^4 + 576430*x^5 + 1641524*x^6 - 22152084*x^7 + 63390443*x^8 + 107381625*x^9 - 1072548108*x^10 + 1604228092*x^11 + 5065000686*x^12 - 19304907936*x^13 + 3650528536*x^14 + 75404779968*x^15 - 99704483296*x^16 - 97719166208*x^17 + 292843382912*x^18 - 76390477824*x^19 - 291118184448*x^20 + 242903138304*x^21 + 32643219456*x^22 - 93923573760*x^23 + 24970788864*x^24))/((1 - 8*x - 14*x^2 + 152*x^3 + 49*x^4 - 816*x^5 - 36*x^6 + 1152*x^7)*(-1 + 40*x - 482*x^2 + 2120*x^3 + 79*x^4 - 26128*x^5 + 55636*x^6 + 29184*x^7 - 170880*x^8 + 112896*x^9)*( - 1 + 20*x - 130*x^2 + 168*x^3 + 1375*x^4 - 4652*x^5 - 348*x^6 + 15472*x^7 - 10816*x^8 - 7296*x^9 + 4608*x^10)).

a(n+1)/a(n) tends to 22.936022136221...

(End)

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, 0):

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

CROSSREFS

Sequence in context: A254681 A219625 A244875 * A219412 A062159 A059721

Adjacent sequences:  A025601 A025602 A025603 * A025605 A025606 A025607

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified May 26 13:59 EDT 2022. Contains 354092 sequences. (Running on oeis4.)