A150516 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, 0, 0), (0, 1, 0), (1, -1, -1), (1, 1, 1)}.

1, 2, 7, 25, 103, 426, 1851, 8108, 36313, 164214, 752101, 3467971, 16108555, 75239742, 353313069, 1666007227, 7885689713, 37449389542, 178386215245, 851949453185, 4078404919005, 19565888530608, 94050288322193, 452884537596804, 2184312630725741, 10550897288768650, 51034231680131937, 247162631307574863

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, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A150513 A150514 A150515 * A150517 A150518 A150519

Adjacent sequences: A150513 A150514 A150515 * A150517 A150518 A150519

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved