A149824 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, -1, 1), (0, 1, 0), (1, 0, 0), (1, 1, -1)}.

1, 2, 4, 10, 28, 82, 276, 950, 3310, 12078, 44530, 166938, 643884, 2497582, 9846816, 39300510, 157864202, 640945466, 2623007032, 10794098482, 44800697192, 186807264986, 783544937362, 3303567503730, 13988690095946, 59491279201242, 254085592304632, 1088721319725422, 4683544234743224

Offset

0,2

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, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A148110 A149823 A192653 * A331938 A302146 A202135

Adjacent sequences: A149821 A149822 A149823 * A149825 A149826 A149827

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved