A148907 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), (-1, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 32, 105, 435, 1585, 6847, 26144, 117306, 463831, 2121051, 8617173, 39898701, 165430592, 773730816, 3259812284, 15362861588, 65556570624, 310851161790, 1340058237363, 6387804534749, 27768944728870, 132962273058794, 582137554477254, 2797765925822252, 12324977210307510, 59420187901561334

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, -1 + j, 1 + 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] + 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: A218882 A148905 A148906 * A148908 A148909 A148910

Adjacent sequences: A148904 A148905 A148906 * A148908 A148909 A148910

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved