A149489 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, 1), (-1, 1, 1), (0, -1, 1), (0, 1, -1), (1, 1, 0)}.

1, 1, 4, 14, 52, 209, 860, 3611, 15470, 67075, 293936, 1299135, 5782369, 25890073, 116507143, 526584341, 2389109731, 10875671609, 49655540621, 227316843705, 1043115351009, 4797021425961, 22103655032502, 102032014882075, 471763934655236, 2184603451900384, 10130495327004170, 47038661457594876

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A284765 A129997 A308023 * A125783 A090319 A295518

Adjacent sequences: A149486 A149487 A149488 * A149490 A149491 A149492

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved