A149428 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, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 4, 13, 44, 156, 560, 2049, 7684, 28772, 108368, 412396, 1573776, 6029488, 23226176, 89573577, 346281380, 1343190436, 5216949776, 20296197484, 79131832976, 308798743728, 1206495306816, 4720960267204, 18487515792272, 72463886990864, 284340829780288, 1116404838166192, 4386449721693760

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, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A252933 A229397 A283110 * A149429 A045652 A149430

Adjacent sequences: A149425 A149426 A149427 * A149429 A149430 A149431

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved