A150132 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, 0, -1), (0, 0, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 6, 20, 72, 267, 1049, 4143, 16949, 69663, 292819, 1233912, 5290492, 22699211, 98729286, 429510950, 1888906238, 8306249099, 36856032199, 163474875090, 730652199324, 3263990655764, 14676974122523, 65958239906224, 298117335758065, 1346561773642717, 6113092353805974, 27733390778583350

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, 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, 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: A360291 A150130 A150131 * A150133 A244783 A216837

Adjacent sequences: A150129 A150130 A150131 * A150133 A150134 A150135

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved