A148551 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, 0), (-1, 1, 1), (1, 0, 0)}.

1, 1, 3, 5, 21, 44, 189, 433, 1975, 4838, 22191, 56451, 265204, 696955, 3285575, 8820421, 42076429, 115141696, 550620015, 1527687361, 7355385064, 20666807843, 99695173095, 282849216712, 1370293182666, 3922714521919, 19033229729799, 54880578183893, 267053279276265, 775197043666002, 3776939545919833

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, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A148548 A148549 A148550 * A148552 A148553 A239795

Adjacent sequences: A148548 A148549 A148550 * A148552 A148553 A148554

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved