A151152 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, 1), (0, 1, 1), (1, 0, 1), (1, 1, 0)}.

1, 3, 11, 47, 207, 932, 4282, 19921, 93514, 442688, 2106609, 10071788, 48346849, 232814651, 1124326965, 5442695967, 26401152237, 128300556743, 624502941066, 3044141919301, 14857912208109, 72602676937685, 355143196039664, 1738884267574347, 8521537513342337, 41794078986552604, 205131804605526962

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A151149 A151150 A151151 * A151153 A151154 A151155

Adjacent sequences: A151149 A151150 A151151 * A151153 A151154 A151155

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved