A150005 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), (-1, 1, -1), (0, 0, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 5, 17, 60, 221, 826, 3229, 12841, 51669, 210672, 870069, 3626280, 15209165, 64286104, 273489917, 1169463848, 5022549846, 21673068761, 93901104376, 408200562527, 1780102962708, 7787537166599, 34163229720947, 150234088468516, 662220519961800, 2925718885996118, 12952307741949492

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + 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: A150002 A150003 A150004 * A150006 A150007 A150008

Adjacent sequences: A150002 A150003 A150004 * A150006 A150007 A150008

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved