A025596 Number of n-move king paths on 8x8 board from given corner to same corner.

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

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: A068776 A355544 A359968 * A172361 A114038 A000222

Adjacent sequences: A025593 A025594 A025595 * A025597 A025598 A025599

Keyword

nonn

Author

David W. Wilson

Status

approved