A148327 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), (0, 0, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 2, 5, 14, 42, 127, 422, 1435, 4840, 17338, 62435, 225190, 837159, 3126319, 11765631, 44783683, 171773846, 664157911, 2575562439, 10077583703, 39670893129, 156317183566, 620651825974, 2475390947605, 9886472711813, 39689896106424, 159948432742012, 645894452400153, 2616112922938863

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, 1 + j, k, -1 + n] + aux[i, 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: A132833 A293347 A148326 * A092493 A316779 A344571

Adjacent sequences: A148324 A148325 A148326 * A148328 A148329 A148330

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved