A150046 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, 0, 1), (-1, 1, 1), (0, 1, 0), (1, 0, 0)}.

1, 2, 6, 18, 60, 213, 783, 2954, 11266, 43797, 172615, 688499, 2767243, 11196425, 45622379, 187050013, 770927359, 3190273470, 13253110663, 55262512845, 231217284417, 970244076921, 4081783249865, 17213974219717, 72764780153769, 308237133128395, 1308193720909185, 5561838577050351

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, j, k, -1 + n] + aux[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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A108531 A150045 A191280 * A009458 A357693 A150047

Adjacent sequences: A150043 A150044 A150045 * A150047 A150048 A150049

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved