A148894 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, 0, 1), (1, -1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 31, 102, 396, 1462, 5997, 23434, 97554, 399179, 1698051, 7092038, 30592688, 130707443, 569802720, 2464058629, 10856547093, 47528837573, 210762034726, 930763267221, 4158095821743, 18498431238161, 83039662287601, 371847601151078, 1677726006526427, 7550315481752813, 34200904355203080

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, 1 + k, -1 + n] + aux[1 + i, 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: A148891 A148892 A148893 * A148895 A148896 A151534

Adjacent sequences: A148891 A148892 A148893 * A148895 A148896 A148897

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved