A148126 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, 0), (-1, 0, -1), (-1, 0, 1), (0, 1, 0), (1, -1, 0)}.

1, 1, 2, 4, 11, 26, 75, 216, 656, 1950, 6394, 20193, 66477, 219595, 751938, 2514386, 8774087, 30337633, 106836045, 374070118, 1345890867, 4774149535, 17280927737, 62313709836, 227984366294, 827225060479, 3057313053045, 11215364858889, 41639840450091, 153962548708726, 576444836942769, 2143059863393340

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A148123 A148124 A148125 * A148127 A148128 A148129

Adjacent sequences: A148123 A148124 A148125 * A148127 A148128 A148129

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved