A150097 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, 0, 1), (0, 0, 1), (0, 1, -1), (1, 0, 0)}.

1, 2, 6, 19, 67, 246, 946, 3738, 15131, 62393, 261234, 1107945, 4748851, 20543866, 89574958, 393287068, 1737215366, 7714927830, 34425987197, 154278363561, 694067730740, 3133405988933, 14191015208980, 64457259869876, 293553080677134, 1340182505670387, 6132274838067467, 28118123306507632

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, 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: A250918 A150095 A150096 * A145847 A150098 A184018

Adjacent sequences: A150094 A150095 A150096 * A150098 A150099 A150100

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved