A150442 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, 1), (0, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 24, 101, 405, 1783, 7591, 34639, 153820, 713327, 3237482, 15230172, 70405231, 333866824, 1560489343, 7455980000, 35199306111, 168979773851, 802989918943, 3872665409915, 18516720913648, 89582113133152, 430171806982270, 2087554276712365, 10065885459201360, 48956423818397154, 236772896209193174

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + 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: A150439 A150440 A150441 * A352906 A150443 A150444

Adjacent sequences: A150439 A150440 A150441 * A150443 A150444 A150445

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved