A149394 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, 1), (0, 1, -1), (0, 1, 1), (1, -1, 1)}.

1, 1, 4, 12, 50, 185, 780, 3204, 13813, 59718, 263526, 1171897, 5271023, 23870426, 108937335, 499859830, 2306602849, 10690798311, 49763016689, 232479087714, 1089750680292, 5123664542506, 24156508140043, 114177433055823, 540919312060295, 2568074656667363, 12216266834710238, 58218376459062370

Offset

0,3

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + 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: A149392 A149393 A104708 * A149395 A149396 A149397

Adjacent sequences: A149391 A149392 A149393 * A149395 A149396 A149397

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved