A150959 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, 0, 1), (1, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 35, 163, 709, 3361, 15335, 73442, 343390, 1655716, 7854801, 38057357, 182269560, 886354596, 4273408701, 20840807280, 100974715750, 493581178083, 2400430534067, 11756143605475, 57343477962594, 281291597405592, 1375364448444273, 6755923683621083, 33098234399346666, 162773883912291350

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, 1 + k, -1 + n] + aux[1 + i, 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: A151309 A150957 A150958 * A150960 A150961 A150962

Adjacent sequences: A150956 A150957 A150958 * A150960 A150961 A150962

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved