A149797 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), (1, -1, 1), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 19, 87, 355, 1671, 7323, 34973, 158775, 764755, 3547363, 17182145, 80837595, 393165213, 1868497093, 9116105897, 43648911963, 213476472531, 1028015717385, 5037664580743, 24368765830921, 119609731099771, 580687465196447, 2854085034956369, 13897292222486197, 68384830086928769

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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, -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: A324595 A275027 A147091 * A149798 A149799 A149800

Adjacent sequences: A149794 A149795 A149796 * A149798 A149799 A149800

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved