A149504 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, 0), (-1, 0, -1), (1, -1, 0), (1, 1, 1)}.

1, 1, 5, 11, 47, 143, 577, 2003, 8189, 29843, 124237, 467583, 1960681, 7577163, 31962501, 125734635, 534229159, 2128096227, 9092397583, 36615310761, 157023171309, 638232284475, 2746009559707, 11244568651801, 48528835473245, 199957782233787, 865169500080713, 3584439532293331

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, k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A106953 A297445 A149503 * A149505 A149506 A149507

Adjacent sequences: A149501 A149502 A149503 * A149505 A149506 A149507

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved