A150408 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), (1, 0, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 24, 94, 365, 1522, 6317, 27305, 117730, 521284, 2305176, 10382686, 46739971, 213238207, 972787925, 4482614090, 20660903549, 95970758823, 445977751724, 2085227368751, 9754995754038, 45861516294520, 215740410214838, 1018995605536144, 4816034636508802, 22838382322351173, 108373516882028634

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, 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: A150406 A150407 A317130 * A150409 A150410 A150411

Adjacent sequences: A150405 A150406 A150407 * A150409 A150410 A150411

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved