A150041 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, 0), (-1, 0, 1), (0, 1, 0), (1, 0, 0)}.

1, 2, 6, 18, 58, 198, 689, 2517, 9252, 34974, 133343, 515540, 2016424, 7938561, 31593267, 126264754, 508683281, 2058402166, 8372464271, 34216910642, 140309572880, 577888143880, 2386568570118, 9890896727268, 41099664145362, 171231491015452, 715238397868050, 2993691546220346

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A293067 A360293 A085139 * A190790 A150042 A351279

Adjacent sequences: A150038 A150039 A150040 * A150042 A150043 A150044

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved