A148534 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, 1, -1), (0, 0, -1), (1, 0, 1)}.

1, 1, 3, 5, 19, 45, 161, 437, 1551, 4933, 17139, 57359, 198625, 705297, 2502895, 8975677, 32125405, 117179077, 431439211, 1588283741, 5873826435, 21780489477, 81834285257, 307828951821, 1160476181565, 4380836478687, 16639698176315, 63583818814709, 243123557763827, 930821719958341, 3571716411859821

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A034511 A133603 A201867 * A148535 A148536 A148537

Adjacent sequences: A148531 A148532 A148533 * A148535 A148536 A148537

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved