A151145 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, 0), (0, 0, -1), (0, 1, 0), (1, 0, 0), (1, 1, 1)}

1, 3, 11, 47, 205, 915, 4197, 19445, 90887, 429091, 2036615, 9711097, 46538103, 223736955, 1078659981, 5215774821, 25273555029, 122695169497, 596801074495, 2907185919885, 14180614357021, 69263754392477, 338679866816603, 1657693556708723, 8121805455346329, 39825586824526497, 195436160696250531

Offset

0,2

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A151142 A151143 A151144 * A151146 A151147 A151148

Adjacent sequences: A151142 A151143 A151144 * A151146 A151147 A151148

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved