A149838 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, 1), (0, 1, 0), (1, 0, 0)}.

1, 2, 4, 12, 36, 100, 340, 1154, 3650, 13244, 47744, 161458, 608218, 2273268, 8015248, 30948100, 118491620, 429836776, 1688856912, 6578861670, 24365169758, 96986976404, 382761606472, 1440159264108, 5790859055340, 23087851622216, 87959372528576, 356553406654718, 1433265655786694, 5515870506340284

Offset

0,2

Links

Table of n, a(n) for n=0..29.

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, j, k, -1 + n] + aux[i, -1 + j, 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, 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: A084716 A241208 A149837 * A192236 A149839 A149840

Adjacent sequences: A149835 A149836 A149837 * A149839 A149840 A149841

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved