A150986 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, 0, 0), (0, -1, 0), (1, 1, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 37, 163, 742, 3417, 15920, 75135, 356274, 1698999, 8146005, 39176567, 188995010, 914447693, 4433447099, 21536356139, 104809992100, 510795470725, 2492722292419, 12180001835433, 59576187799646, 291691287247123, 1429462763111044, 7010807607813331, 34410279282825758, 169010343748395951

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, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A150983 A150984 A150985 * A150987 A150988 A150989

Adjacent sequences: A150983 A150984 A150985 * A150987 A150988 A150989

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved