A149969 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), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 5, 16, 55, 195, 719, 2680, 10130, 38717, 148870, 576483, 2242586, 8757737, 34320069, 134835020, 530974983, 2094950165, 8278736511, 32762059345, 129804162885, 514821301922, 2043694619332, 8119201783320, 32278332330007, 128401708226616, 511048860567376, 2034979608372275

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[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: A363201 A321470 A149968 * A051960 A149970 A157418

Adjacent sequences: A149966 A149967 A149968 * A149970 A149971 A149972

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved