A149579 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), (0, -1, 0), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 15, 51, 211, 817, 3079, 13389, 54809, 220007, 973339, 4116547, 17086809, 76513949, 330153771, 1400440409, 6324959359, 27671023795, 119172354919, 541697331769, 2393897850853, 10427208639551, 47633940790113, 212143334646493, 932171574620567, 4275491555247375, 19158820802260561

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[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: A149576 A149577 A149578 * A149580 A099834 A034537

Adjacent sequences: A149576 A149577 A149578 * A149580 A149581 A149582

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved