A108694 Triangle T(n,k), 0<=k<=n, read by rows, given by [1, 2, 2, 4, 3, 6, 4, 8, 5, 10, 6, 12, . . . ] DELTA [2, 1, 4, 2, 6, 3, 8, 4, 10, 5, 12, 6, . . . ] where DELTA is the operator defined in A084938.

1, 1, 2, 3, 9, 6, 13, 54, 69, 26, 75, 399, 747, 573, 150, 541, 3508, 8638, 9998, 5393, 1082, 4683, 35817, 109248, 169038, 139143, 57585, 9366, 47293, 416762, 1515531, 2935222, 3256907, 2064534, 691645, 94586

Offset

0,3

Comments

Related to preferential arrangements of n elements (A000670) and necklaces of sets of labeled beads (A000629).

Links

Table of n, a(n) for n=0..35.

Formula

Sum_{ k>=0 } T(n, k) = n!*3^n = A032031(n).

T(n, 0) = A000670(n); T(n, n) = A000629(n).

Example

1; 1, 2; 3, 9, 6; 13, 54, 69, 26; 75, 399, 747, 573, 150; ...

Crossrefs

Cf. A000629, A000670, A032031, A084938.

Sequence in context: A011028 A224519 A288842 * A267896 A199858 A357053

Adjacent sequences: A108691 A108692 A108693 * A108695 A108696 A108697

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Jun 18 2005

Status

approved