A149311 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), (0, 1, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 11, 48, 179, 803, 3347, 15405, 67615, 316818, 1433550, 6798291, 31384353, 150127852, 702876838, 3383981344, 16008320227, 77451059648, 369297451020, 1793610956069, 8605162604201, 41922759352846, 202126340881473, 987203746158647, 4778839068108031, 23389103742765915, 113597331041042258

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[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: A149309 A372115 A149310 * A212086 A361359 A296532

Adjacent sequences: A149308 A149309 A149310 * A149312 A149313 A149314

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved