A150736 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, 0), (0, 1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 29, 122, 516, 2252, 10061, 45338, 207471, 956325, 4442616, 20775644, 97621228, 460944623, 2184762361, 10390395273, 49569323130, 237091907445, 1136794003705, 5462262285041, 26296634932742, 126823383793412, 612613444030350, 2963558441001062, 14355667355543549, 69625744702294649

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A150733 A150734 A150735 * A150737 A150738 A150739

Adjacent sequences: A150733 A150734 A150735 * A150737 A150738 A150739

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved