A149923 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), (0, 1, 0), (1, 0, -1), (1, 0, 0)}.

1, 2, 5, 15, 47, 159, 567, 2079, 7920, 30827, 122432, 495884, 2034691, 8466701, 35632214, 151397685, 649417899, 2806992134, 12221505766, 53565228368, 236125050931, 1046671869520, 4662417859457, 20863697406632, 93761573243960, 422995742344138, 1915298621788458, 8701706539380666

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[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 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: A149922 A192053 A013560 * A219231 A149924 A149925

Adjacent sequences: A149920 A149921 A149922 * A149924 A149925 A149926

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved