A148699 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), (1, 1, 0)}.

1, 1, 3, 7, 23, 69, 229, 721, 2541, 8240, 29393, 98714, 355194, 1216839, 4415474, 15380589, 56058177, 197157783, 723355013, 2565493440, 9440747457, 33741764503, 124548794972, 447786779945, 1657037091434, 5989639030646, 22208645758296, 80596640887627, 299496377454683, 1090864144257659, 4059670690241188

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, 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: A148696 A148697 A148698 * A181999 A148700 A151268

Adjacent sequences: A148696 A148697 A148698 * A148700 A148701 A148702

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved