A150963 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, 1), (-1, 1, 1), (1, 0, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 35, 166, 727, 3548, 16332, 80629, 381024, 1891196, 9076846, 45180577, 219017831, 1091957861, 5329439061, 26597315767, 130440635128, 651386378673, 3205983917849, 16016254589193, 79041771645231, 394976235966847, 1953333859377909, 9762652876280494, 48360717772934649, 241733414225774238

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, -1 + j, 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, -1 + 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: A150960 A150961 A150962 * A150964 A150965 A150966

Adjacent sequences: A150960 A150961 A150962 * A150964 A150965 A150966

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved