

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
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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/(1sum(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 <= n1} a(ns)*b(s) for n>=2, where b(n) = Sum_{mn} (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



