A150871 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, 1, 1), (1, -1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 8, 33, 145, 660, 3071, 14512, 69325, 333898, 1618263, 7881459, 38534551, 188997127, 929341022, 4579498427, 22606465741, 111763160068, 553246380277, 2741655639332, 13599288377502, 67510923124446, 335382956357382, 1667165270794207, 8291908591873207, 41261097646111480, 205406246622285068

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, k, -1 + n] + aux[i, -1 + 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: A150868 A150869 A150870 * A150872 A150873 A150874

Adjacent sequences: A150868 A150869 A150870 * A150872 A150873 A150874

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved