A149347 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, 1), (-1, 1, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 42, 151, 578, 2213, 8692, 34390, 138697, 560620, 2289920, 9390621, 38814879, 160867961, 670118507, 2799480186, 11742654551, 49366635903, 208158082202, 879572305693, 3725842253287, 15810471546038, 67223687535656, 286282793431227, 1221244261088140, 5216874884788580

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A100217 A149345 A149346 * A173411 A149348 A149349

Adjacent sequences: A149344 A149345 A149346 * A149348 A149349 A149350

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved