A151069 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, 1, -1), (0, 1, 0), (0, 1, 1), (1, 0, 0)}.

1, 3, 10, 39, 161, 677, 2944, 13043, 58346, 264572, 1210963, 5575702, 25857861, 120582205, 564582762, 2655193678, 12532838999, 59328877385, 281701560204, 1341028983984, 6397896935932, 30590330691361, 146545757482318, 703235343882409, 3380254025327490, 16272430961904116, 78441250955939205

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + 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: A123768 A005750 A151068 * A151070 A151071 A063022

Adjacent sequences: A151066 A151067 A151068 * A151070 A151071 A151072

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved