A148804 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, 0, 0), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 26, 83, 286, 981, 3493, 12469, 45525, 166624, 618123, 2300128, 8638210, 32528611, 123266486, 468285464, 1787276670, 6836101525, 26237809440, 100895198047, 389029486532, 1502466389904, 5814999975045, 22537930750295, 87503846935743, 340155623048742, 1324169995953546, 5160356768069861

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A255712 A194690 A148803 * A148805 A000237 A148806

Adjacent sequences: A148801 A148802 A148803 * A148805 A148806 A148807

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved