A148259 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), (0, 1, 1), (1, -1, 0)}.

1, 1, 2, 4, 14, 32, 109, 299, 1084, 3139, 11753, 35842, 137532, 434036, 1690951, 5507642, 21687826, 72175581, 287446781, 973876954, 3911669188, 13451568636, 54391647165, 189561457959, 770748855265, 2715542904809, 11098722287506, 39475545312252, 162064280826549, 581219175969977, 2395244255294436

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, 1 + j, 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, -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: A129744 A148257 A148258 * A148260 A148261 A148262

Adjacent sequences: A148256 A148257 A148258 * A148260 A148261 A148262

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved