A149613 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, -1), (1, -1, 1), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 15, 63, 239, 1051, 4373, 19545, 85189, 387733, 1736045, 8005589, 36495147, 170006871, 785147059, 3686227031, 17192251653, 81223958909, 381743322857, 1812787977113, 8572561077555, 40882639386795, 194310303523333, 930015526055741, 4438917935359283, 21311390117273367, 102081925144318685

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A149610 A149611 A149612 * A149614 A149615 A149616

Adjacent sequences: A149610 A149611 A149612 * A149614 A149615 A149616

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved