A150090 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, 1, 0), (0, 1, 0), (1, 0, -1), (1, 1, 0)}.

1, 2, 6, 19, 66, 243, 930, 3677, 14911, 61634, 259234, 1105147, 4767937, 20782106, 91385250, 405000507, 1807317447, 8114777154, 36636893847, 166234252180, 757672572779, 3467591514145, 15929670995318, 73431924702453, 339581832393760, 1575001867846787, 7324903642155787, 34152593363634683

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, 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] + 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: A150087 A150088 A150089 * A150091 A190737 A150092

Adjacent sequences: A150087 A150088 A150089 * A150091 A150092 A150093

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved