A148394 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), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 5, 16, 52, 188, 673, 2528, 9448, 36232, 138642, 538502, 2089746, 8183600, 32039011, 126154812, 496759140, 1963415328, 7761746678, 30760767292, 121938877154, 484214723920, 1923302168038, 7648666905624, 30425224701788, 121132809344714, 482381656899028, 1922197151700130

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, 1 + j, -1 + k, -1 + n] + aux[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: A149956 A149957 A148393 * A291685 A268571 A001428

Adjacent sequences: A148391 A148392 A148393 * A148395 A148396 A148397

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved