A149566 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, 1, -1), (-1, 1, 1), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 13, 59, 197, 921, 3331, 15865, 60727, 290761, 1154769, 5566691, 22646317, 109734289, 454966047, 2212275089, 9308019727, 45397584033, 193256139843, 944805547085, 4061502079851, 19894633979005, 86223586271699, 423054029104429, 1846333654372483, 9071603795114213, 39830702967754297

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149563 A149564 A149565 * A298066 A298715 A006701

Adjacent sequences: A149563 A149564 A149565 * A149567 A149568 A149569

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved