A148272 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), (-1, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 15, 39, 151, 433, 1737, 5364, 22286, 72471, 307379, 1035102, 4443074, 15382530, 66756535, 236379784, 1034933583, 3731202187, 16442311519, 60176605412, 266663158823, 988613764004, 4402174929833, 16501712222711, 73776677838972, 279222682669813, 1252736192820485, 4781601894521197

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[1 + 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: A148269 A148270 A148271 * A148273 A148274 A148275

Adjacent sequences: A148269 A148270 A148271 * A148273 A148274 A148275

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved