A149503 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, 0), (-1, -1, 1), (-1, 0, 0), (0, -1, 0), (1, 1, 0)}.

1, 1, 5, 11, 47, 143, 555, 1981, 7477, 28549, 108961, 426105, 1662133, 6568089, 26088533, 104028671, 418100919, 1683005799, 6816895227, 27676678867, 112793176879, 461118216915, 1889680551359, 7767367649263, 31991637007963, 132086685745455, 546431369722467, 2264882999794055

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, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A079029 A106953 A297445 * A149504 A149505 A149506

Adjacent sequences: A149500 A149501 A149502 * A149504 A149505 A149506

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved