A150229 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, 0, 0), (0, 0, 1), (1, -1, 0), (1, 1, 0)}.

1, 2, 6, 22, 80, 310, 1252, 5148, 21482, 91276, 392896, 1701500, 7442013, 32815590, 145380566, 647569948, 2900243037, 13040713888, 58828778368, 266395866595, 1210193354780, 5510852683899, 25161291048035, 115172327913152, 528225223735864, 2427259219164773, 11175758755982136, 51542960940788254

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, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A206304 A201372 A072547 * A150230 A360266 A360290

Adjacent sequences: A150226 A150227 A150228 * A150230 A150231 A150232

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved