A149025 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), (0, 1, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 3, 9, 38, 140, 604, 2449, 10927, 46990, 214160, 949940, 4396411, 19899975, 93160452, 428506551, 2022890300, 9411578929, 44720051414, 209872108538, 1002525113773, 4739546631453, 22736550385796, 108110600640944, 520463523561756, 2486388168617500, 12006128842805812, 57592279400912576

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[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: A047148 A149023 A149024 * A351070 A346056 A133222

Adjacent sequences: A149022 A149023 A149024 * A149026 A149027 A149028

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved