A150071 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), (0, 0, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 6, 18, 64, 220, 792, 2844, 10508, 38726, 144976, 542780, 2051752, 7761764, 29554000, 112658878, 431389136, 1653790724, 6360803312, 24493717106, 94551791464, 365396555846, 1414800367992, 5483604012036, 21286461979104, 82707275267172, 321758489858736, 1252797572552836, 4883010365872848

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A150068 A150069 A150070 * A265945 A007454 A305578

Adjacent sequences: A150068 A150069 A150070 * A150072 A150073 A150074

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved