A149590 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), (-1, 0, 0), (0, -1, 0), (0, 0, -1), (1, 1, 1)}

1, 1, 5, 15, 57, 217, 863, 3437, 14245, 58719, 248277, 1047681, 4500453, 19296867, 83883423, 364076061, 1597411029, 6999282601, 30941709011, 136616489201, 607700266033, 2700153649275, 12073795188291, 53931950506355, 242236477166959, 1086946964513947, 4900932467767547, 22077413679763581

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[i, j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, 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: A203294 A149589 A110614 * A149591 A149592 A149593

Adjacent sequences: A149587 A149588 A149589 * A149591 A149592 A149593

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved