A150796 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, 0, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 31, 131, 568, 2533, 11484, 52740, 244775, 1145293, 5394930, 25554213, 121607175, 581024653, 2785571235, 13394614382, 64577293261, 312054970029, 1511030471653, 7330114769771, 35617526665405, 173325534721156, 844592645777094, 4120649579279555, 20126665956239621, 98406880864109995

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + 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: A150794 A150795 A027078 * A150797 A150798 A150799

Adjacent sequences: A150793 A150794 A150795 * A150797 A150798 A150799

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved