A150188 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, -1, 1), (0, 0, 1), (1, 1, 0)}.

1, 2, 6, 21, 77, 294, 1176, 4763, 19717, 82867, 351623, 1508591, 6523496, 28396178, 124410591, 547816367, 2423461096, 10766562754, 48003764190, 214752543843, 963633578716, 4335715376201, 19557245074613, 88419476924596, 400594258928572, 1818505891287829, 8270074885487383, 37673616875532497

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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + 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: A294048 A375443 A063023 * A150189 A144169 A355152

Adjacent sequences: A150185 A150186 A150187 * A150189 A150190 A150191

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved