A149149 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), (-1, 1, -1), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 9, 38, 111, 489, 1611, 7292, 25865, 119229, 444481, 2075488, 8019353, 37805228, 150069461, 712667390, 2889197265, 13800198063, 56900245013, 273057703416, 1141558272143, 5499371173998, 23258138316869, 112406688710300, 480068721208329, 2326541496532377, 10019955108804655, 48673791102092756

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149146 A149147 A149148 * A149150 A149151 A149152

Adjacent sequences: A149146 A149147 A149148 * A149150 A149151 A149152

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved