A150791 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, 0, -1), (1, 0, 1), (1, 1, 0)}

1, 2, 8, 30, 137, 589, 2808, 12781, 62089, 291115, 1428284, 6816121, 33635236, 162350760, 804067233, 3911333464, 19418285920, 94983590146, 472344514041, 2319909376113, 11550436450930, 56905722036649, 283571424065622, 1400435947285545, 6983194116794444, 34552479396503404, 172380221783627793

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[-1 + i, 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: A150788 A150789 A150790 * A026693 A150792 A302187

Adjacent sequences: A150788 A150789 A150790 * A150792 A150793 A150794

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved