A149253 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, 0), (-1, 1, 1), (0, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 38, 138, 518, 1909, 7396, 29004, 114650, 458976, 1855190, 7520248, 30736206, 126536623, 522647762, 2167449134, 9030785432, 37737890674, 158149549188, 664941243940, 2802641939970, 11837911798350, 50119400695692, 212621399697570, 903524569003676, 3846314336982234

Offset

0,3

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, 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, 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: A149250 A149251 A149252 * A149254 A149255 A149256

Adjacent sequences: A149250 A149251 A149252 * A149254 A149255 A149256

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved