A148829 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, 1, -1), (1, -1, -1), (1, 0, 1)}.

1, 1, 3, 8, 27, 87, 324, 1157, 4635, 17413, 71379, 282310, 1184826, 4816221, 20574697, 85413385, 370033453, 1564014542, 6843477551, 29329378121, 129458112478, 561010625695, 2494707083517, 10912958247500, 48821550558187, 215277199846751, 968129245448296, 4297953300845067, 19417665080599818

Offset

0,3

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[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + 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: A148826 A148827 A148828 * A148830 A148831 A029892

Adjacent sequences: A148826 A148827 A148828 * A148830 A148831 A148832

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved