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A106361 Number of rooted ordered trees where no branch is identical to its adjacent neighbor. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A202846 A107269 A086811 * A113040 A244036 A220184

Adjacent sequences:  A106358 A106359 A106360 * A106362 A106363 A106364

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower, Apr 29 2005

STATUS

approved

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Last modified October 18 07:58 EDT 2019. Contains 328146 sequences. (Running on oeis4.)