A149443 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, 0, 1), (0, -1, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 13, 47, 190, 763, 3227, 13927, 60718, 270671, 1215297, 5514230, 25266201, 116347060, 539873745, 2516929673, 11787991535, 55463882701, 261804584175, 1240265555449, 5892529135236, 28069611267573, 134054703500009, 641577591353535, 3077013944343179, 14784766543766619, 71160899170055625

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149442 A078468 A354339 * A125656 A279159 A351509

Adjacent sequences: A149440 A149441 A149442 * A149444 A149445 A149446

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved