A150321 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, -1), (-1, 1, 1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 21, 93, 334, 1545, 5904, 28361, 113885, 551115, 2267035, 11116928, 46792329, 229966829, 980712270, 4849282854, 20956092385, 103706253002, 451920681361, 2243783211929, 9862687093128, 48985163274870, 216579668572023, 1077789377046301, 4794449369040784, 23862905082085041, 106615213319244750

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150318 A150319 A150320 * A076716 A088591 A229493

Adjacent sequences: A150318 A150319 A150320 * A150322 A150323 A150324

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved