A149538 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, -1, 1), (1, 1, 1)}

1, 1, 5, 13, 51, 179, 707, 2631, 10657, 41565, 169377, 678979, 2805783, 11404107, 47516901, 195827851, 820726217, 3412550073, 14390982059, 60257900655, 255171625883, 1075127342833, 4570044063309, 19344638669811, 82504699986853, 350671396291897, 1499645586308341, 6396288907426213

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, 1 + 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: A243304 A238508 A151274 * A149539 A007231 A158345

Adjacent sequences: A149535 A149536 A149537 * A149539 A149540 A149541

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved