A149749 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, 1), (-1, 1, 0), (1, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 81, 317, 1537, 6553, 32093, 143493, 706865, 3253045, 16084801, 75439549, 373966353, 1777282613, 8826387409, 42353608637, 210621679933, 1018027136981, 5067758038661, 24632141537281, 122716063253689, 599102485940953, 2986546886121353, 14631911369167485, 72976545797444585

Offset

0,3

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A053418 A151882 A359206 * A149750 A179605 A149751

Adjacent sequences: A149746 A149747 A149748 * A149750 A149751 A149752

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved