A150114 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), (0, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 2, 6, 19, 70, 263, 1039, 4201, 17360, 72965, 310840, 1338571, 5820669, 25504666, 112537658, 499493326, 2228445752, 9988153191, 44949498534, 203026168336, 920042020632, 4181646741701, 19057370396166, 87065535081027, 398665735321696, 1829253321634891, 8409472030816278, 38728745148056846

Offset

0,2

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, j, 1 + k, -1 + n] + aux[i, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A150111 A150112 A150113 * A199128 A150115 A177477

Adjacent sequences: A150111 A150112 A150113 * A150115 A150116 A150117

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved