A148280 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, -1, 1), (-1, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 16, 46, 193, 622, 2701, 9325, 42182, 154184, 711849, 2705836, 12670859, 49549930, 234642749, 938567225, 4481414935, 18256143420, 87727604158, 362745516847, 1752161026619, 7335659037548, 35582376864192, 150551110627071, 732790706277408, 3128696622216073, 15272684090284663

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A370658 A148279 A101061 * A112638 A077162 A128903

Adjacent sequences: A148277 A148278 A148279 * A148281 A148282 A148283

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved