A149119 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, 0, 1), (0, -1, 0), (1, 1, 0)}.

1, 1, 4, 9, 32, 103, 361, 1291, 4776, 17539, 67577, 255967, 1001804, 3907961, 15484786, 61440637, 246958922, 990680625, 4026610245, 16324121493, 66857579486, 273568388471, 1127916470190, 4647900956921, 19282067260636, 79920524162991, 333276886331913, 1388649016525857, 5815906328368270

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, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A149116 A149117 A149118 * A149120 A219151 A057819

Adjacent sequences: A149116 A149117 A149118 * A149120 A149121 A149122

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved