A149788 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, -1, 0), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 83, 353, 1589, 7145, 32933, 152447, 714599, 3361687, 15928719, 75738541, 361870393, 1733808857, 8335129385, 40163623975, 194021262095, 939043445935, 4553722647087, 22117204609869, 107589526912129, 524056837438739, 2555867622013271, 12478986518086861, 60993027199021313, 298394251736402297

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 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: A323267 A340736 A094726 * A149789 A149790 A017963

Adjacent sequences: A149785 A149786 A149787 * A149789 A149790 A149791

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved