A149580 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), (1, -1, 0), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 15, 51, 211, 839, 3101, 13777, 56029, 225753, 998649, 4259533, 17547961, 79246365, 341317867, 1447967799, 6547005707, 28728690943, 123265763859, 562522396495, 2483979626475, 10811234059495, 49435750692095, 220413570022171, 966302949202591, 4441088985762059, 19891117970945135

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, 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: A149577 A149578 A149579 * A099834 A034537 A318493

Adjacent sequences: A149577 A149578 A149579 * A149581 A149582 A149583

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved