A151064 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, -1, 0), (0, 0, 1), (0, 1, 1), (1, 1, 0)}.

1, 3, 10, 39, 156, 642, 2722, 11667, 50698, 222694, 984882, 4388122, 19660792, 88498016, 400130204, 1815615083, 8265315422, 37738357610, 172749251346, 792644489638, 3644770466896, 16791898728456, 77501095867108, 358282934471174, 1658822488401828, 7691017667622796, 35705237733616036

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A149050 A300974 A149051 * A151065 A151066 A151067

Adjacent sequences: A151061 A151062 A151063 * A151065 A151066 A151067

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved