A149759 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, 0, 0), (0, -1, 0), (0, 1, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 19, 71, 287, 1211, 5209, 22433, 97741, 431877, 1921997, 8605981, 38690161, 174755445, 793122851, 3611837535, 16499831447, 75559798515, 346876213967, 1596359816971, 7361342844775, 34008838169115, 157366474726651, 729297458819767, 3384981878898179, 15731819597690843, 73204456226077479

Offset

0,3

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, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A001834 A099393 A083588 * A149760 A149761 A149762

Adjacent sequences: A149756 A149757 A149758 * A149760 A149761 A149762

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved