A150052 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, 0), (-1, 1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 6, 18, 62, 207, 752, 2640, 9851, 35585, 134948, 496518, 1902953, 7091719, 27380535, 103001513, 399825496, 1514917496, 5904531754, 22498898512, 87970348703, 336742579350, 1319994431360, 5071911065900, 19922270101843, 76791302296540, 302146083406095, 1167774135013817, 4601313064976307

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, -1 + j, 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, 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: A177473 A177471 A303117 * A262590 A150053 A150054

Adjacent sequences: A150049 A150050 A150051 * A150053 A150054 A150055

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved