A149960 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), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 5, 16, 54, 186, 663, 2388, 8749, 32509, 121494, 457682, 1733295, 6595168, 25218573, 96727444, 372169841, 1435821588, 5551953314, 21517134765, 83539873826, 324881623016, 1265367151107, 4934999346299, 19271606653792, 75340504847674, 294838274252009, 1154921735775714, 4527891707197426

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, 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: A149959 A161941 A120899 * A149961 A141754 A149962

Adjacent sequences: A149957 A149958 A149959 * A149961 A149962 A149963

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved