A150567 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, 0, 0), (0, 0, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 26, 107, 457, 2016, 9065, 41424, 191529, 894019, 4204565, 19897098, 94641154, 452107980, 2167676408, 10425903303, 50282484818, 243082789531, 1177611502760, 5715528217575, 27786221354972, 135284133335976, 659545295681644, 3219346412950448, 15731435487175994, 76949340577947377

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150564 A150565 A150566 * A000151 A150568 A102319

Adjacent sequences: A150564 A150565 A150566 * A150568 A150569 A150570

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved