A149484 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), (-1, 1, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 58, 231, 1084, 4728, 22723, 103602, 504562, 2361704, 11593006, 55174776, 272199900, 1310139935, 6485171356, 31463283353, 156106431306, 761779721856, 3785937470147, 18555926973117, 92334192444210, 454082613214306, 2261613072534943, 11151639371837816, 55581684676610844, 274642522606342851

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[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + 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: A149481 A149482 A149483 * A149485 A006798 A158267

Adjacent sequences: A149481 A149482 A149483 * A149485 A149486 A149487

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved