A150019 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), (-1, 1, -1), (0, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 5, 18, 66, 250, 998, 4010, 16537, 69342, 293458, 1257093, 5424876, 23588068, 103233879, 454308177, 2009507717, 8926272795, 39812543051, 178190481133, 800159369179, 3603867667219, 16274928666567, 73684182750185, 334362668167067, 1520532623466630, 6928507283774292, 31628926838053398

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A150016 A150017 A150018 * A005753 A150020 A144721

Adjacent sequences: A150016 A150017 A150018 * A150020 A150021 A150022

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved