A150189 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), (1, -1, 1), (1, 1, 0)}.

1, 2, 6, 21, 77, 300, 1205, 4953, 20803, 88398, 380885, 1655075, 7254932, 32022552, 142171030, 634730173, 2846078283, 12817275806, 57925380570, 262668322805, 1194631478606, 5447802555181, 24905877854090, 114113876272866, 523959177617163, 2410307692682842, 11107724672261045, 51273047125023219

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[-1 + 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: A375443 A063023 A150188 * A144169 A355152 A363813

Adjacent sequences: A150186 A150187 A150188 * A150190 A150191 A150192

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved