A149971 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, 0, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 5, 16, 55, 202, 788, 3164, 13059, 55076, 236334, 1029234, 4535902, 20200270, 90758717, 410933676, 1873206910, 8589677654, 39597122282, 183397246362, 853021434437, 3982738734064, 18659695033482, 87698406837964, 413356798353195, 1953440656251830, 9253901949698603, 43935669050478198

Offset

0,2

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, -1 + 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: A051960 A149970 A157418 * A176828 A149972 A026106

Adjacent sequences: A149968 A149969 A149970 * A149972 A149973 A149974

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved