A150811 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, 1, 1), (0, 1, -1), (1, 0, 0), (1, 1, 1)}

1, 2, 8, 31, 134, 591, 2671, 12241, 56897, 266408, 1258036, 5971141, 28484881, 136422997, 655618049, 3159999564, 15269565860, 73948510773, 358825922576, 1744183807179, 8491361315479, 41396815400461, 202071596590831, 987504956128548, 4830876442260184, 23655190097709336, 115932847417593590

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A150808 A150809 A150810 * A150812 A150813 A150814

Adjacent sequences: A150808 A150809 A150810 * A150812 A150813 A150814

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved