A148180 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, -1, 0), (-1, 1, 0), (1, -1, 1), (1, 0, 0)}.

1, 1, 2, 4, 12, 28, 92, 251, 860, 2513, 9147, 28003, 104286, 332940, 1264621, 4143576, 16059654, 53812043, 210796710, 719697420, 2851086259, 9873316114, 39477178907, 138480427194, 557399401255, 1976326100848, 8008908870844, 28656426926198, 116748517621235, 421186490480246, 1723888841623296

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A080876 A148178 A148179 * A148181 A331687 A148182

Adjacent sequences: A148177 A148178 A148179 * A148181 A148182 A148183

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved