A148893 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), (0, -1, 1), (0, 1, 1), (1, 1, -1)}.

1, 1, 3, 8, 31, 102, 392, 1454, 5890, 23160, 95273, 392398, 1649111, 6924724, 29550882, 126827458, 547935967, 2378179558, 10398410511, 45643035246, 201086177071, 889753284580, 3953260596886, 17612836079032, 78700941911642, 352786193448388, 1585438179980456, 7140136013364276, 32233140285510131

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[i, -1 + j, -1 + k, -1 + n] + aux[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: A148890 A148891 A148892 * A148894 A148895 A148896

Adjacent sequences: A148890 A148891 A148892 * A148894 A148895 A148896

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved