A149157 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 0), (-1, 1, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 9, 39, 112, 514, 1664, 7833, 27346, 130723, 479977, 2317526, 8827710, 42919942, 168085941, 821366455, 3287613734, 16126250115, 65690433233, 323170950475, 1335621327595, 6586014226736, 27550903813319, 136109790047564, 575278188394020, 2846407705761070, 12137734111711302, 60132476045010784

Offset

0,3

Links

Table of n, a(n) for n=0..28.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149154 A149155 A149156 * A149158 A142239 A118639

Adjacent sequences: A149154 A149155 A149156 * A149158 A149159 A149160

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved