A150242 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, 0, 0), (0, 1, 1), (1, 0, -1), (1, 0, 0)}.

1, 2, 6, 22, 83, 333, 1381, 5825, 25211, 110375, 489231, 2193431, 9902749, 45080215, 206453882, 950527781, 4399269168, 20442141063, 95371321258, 446489207904, 2096669042415, 9874851742970, 46626057108520, 220685689561458, 1046828402337235, 4975577119808990, 23693924168707335, 113025905703829794

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, 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] + 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: A150239 A150240 A150241 * A150243 A200316 A164870

Adjacent sequences: A150239 A150240 A150241 * A150243 A150244 A150245

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved