A150790 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), (1, 0, 1), (1, 1, -1), (1, 1, 0)}

1, 2, 8, 30, 137, 588, 2806, 12733, 61872, 289164, 1418356, 6747493, 33281782, 160181469, 792919129, 3847160244, 19089911001, 93165068531, 463075455779, 2269853477049, 11296127261782, 55555915252335, 276731864895618, 1364580711769992, 6801904629731614, 33610790605776993, 167627286021715992

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 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: A150787 A150788 A150789 * A150791 A026693 A150792

Adjacent sequences: A150787 A150788 A150789 * A150791 A150792 A150793

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved