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A025596 Number of n-move king paths on 8x8 board from given corner to same corner. 2
1, 0, 3, 6, 38, 160, 905, 4830, 28308, 166992, 1024758, 6389460, 40724244, 263385408, 1728855843, 11484066594, 77129083947, 522959361936, 3576364370022, 24643554967656, 170964572526549, 1193217941096604, 8372537679729462, 59027518046416656, 417904230297222132 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

FORMULA

G.f.: (366792*x^28 +1467576*x^27 -12798504*x^26 -72600752*x^25 -21006456*x^24 +422686650*x^23 +540127006*x^22 -778634925*x^21 -1667725833*x^20 +251744543*x^19 +2041143680*x^18 +623336211*x^17 -1120415212*x^16 -632536275*x^15 +292599456*x^14 +251183915*x^13 -34444590*x^12 -53894715*x^11 +598372*x^10 +6991156*x^9 +261765*x^8 -576944*x^7 -24270*x^6 +30477*x^5 +523*x^4 -963*x^3 +24*x^2+14*x-1) / ((3*x-1) *(x +1) *(3*x^3-3*x-1) *(x^3-3*x+1) *(17*x^3+6*x^2-3*x-1) *(x^3+3*x^2-6*x+1) *(3*x^3+9*x^2+6*x-1) *(19*x^3-9*x^2-3*x+1) *(x^3+9*x^2+6*x+1) *(3*x^3-9*x^2-3*x+1) *(17*x^3+18*x^2+3*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$3],

       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, 0, 0):

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

CROSSREFS

Sequence in context: A211893 A093800 A068776 * A172361 A114038 A000222

Adjacent sequences:  A025593 A025594 A025595 * A025597 A025598 A025599

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified April 3 01:31 EDT 2020. Contains 333195 sequences. (Running on oeis4.)