A148203 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, 0, 1), (1, -1, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 12, 34, 117, 385, 1432, 5160, 20168, 77045, 311677, 1239448, 5140477, 21049400, 88974654, 372438423, 1597803426, 6803880625, 29540393405, 127517380748, 559088380312, 2440361663214, 10787438980198, 47519879806761, 211517358073448, 938964601279267, 4204355678918899

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, 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, 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: A148200 A148201 A148202 * A240904 A245310 A363202

Adjacent sequences: A148200 A148201 A148202 * A148204 A148205 A148206

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved