A106361 Number of rooted ordered trees where no branch is identical to its adjacent neighbor.

1, 1, 1, 3, 6, 16, 45, 128, 371, 1106, 3343, 10230, 31635, 98714, 310366, 982437, 3128051, 10011848, 32193840, 103955571, 336946034, 1095873115, 3575319049, 11697938232, 38374479841, 126190075741, 415889689954, 1373506798548

Offset

1,4

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Index entries for sequences related to rooted trees

Formula

Shifts left under Carlitz transform.

Carlitz transform T(A(x)) has g.f. 1/(1-sum(k>0, (-1)^(k+1)*A(x^k))).

From Petros Hadjicostas, Sep 17 2017: (Start)

The following results are simple consequences of the fact that the sequence shifts left under the Carlitz transform.

a(n) = Sum_{1 <= s <= n-1} a(n-s)*b(s) for n>=2, where b(n) = Sum_{m|n} (-1)^{1+(n/m)} a(m), with a(1) = 1.

If A(x) = Sum_{n>=1} a(n)*x^n, then A(x)-x = A(x)*Sum_{n>=1} a(n)*x^n/(1+x^n).

(End)

Crossrefs

Cf. A000081, A106362, A106363.

Sequence in context: A107269 A333026 A086811 * A113040 A244036 A220184

Adjacent sequences: A106358 A106359 A106360 * A106362 A106363 A106364

Keyword

nonn,eigen

Author

Christian G. Bower, Apr 29 2005

Status

approved