A148710 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, 0, 0), (-1, 1, 1), (0, -1, 0), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 7, 23, 75, 265, 967, 3612, 13881, 54146, 215339, 867249, 3535563, 14566079, 60517102, 253570701, 1069568322, 4541585236, 19392943306, 83243237160, 359033012893, 1555119755691, 6763331933677, 29520138529918, 129292173036870, 568043777594337, 2503024585782289, 11059575161062936

Offset

0,3

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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148707 A148708 A148709 * A148711 A344775 A205481

Adjacent sequences: A148707 A148708 A148709 * A148711 A148712 A148713

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved