login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A317100 Number of series-reduced planted achiral trees with n leaves spanning an initial interval of positive integers. 4
1, 3, 5, 12, 17, 41, 65, 144, 262, 533, 1025, 2110, 4097, 8261, 16407, 32928, 65537, 131384, 262145, 524854, 1048647, 2098181, 4194305, 8390924, 16777234, 33558533, 67109132, 134226070, 268435457, 536887919, 1073741825, 2147516736, 4294968327, 8590000133 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In these trees, achiral means that all branches directly under any given node that is not a leaf or a cover of leaves are equal, and series-reduced means that every node that is not a leaf or a cover of leaves has at least two branches.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

FORMULA

a(n) ~ 2^(n-1). - Vaclav Kotesovec, Sep 07 2019

EXAMPLE

The a(4) = 12 trees:

  (1111), ((11)(11)), (((1)(1))((1)(1))), ((1)(1)(1)(1)),

  (1222),

  (1122), ((12)(12)),

  (1112),

  (1233),

  (1223),

  (1123),

  (1234).

MATHEMATICA

allnorm[n_Integer]:=Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1];

b[n_]:=1+Sum[b[n/d], {d, Rest[Divisors[n]]}];

a[n_]:=Sum[b[GCD@@Length/@Split[ptn]], {ptn, allnorm[n]}];

Array[a, 10]

PROG

(PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n]=2^(n-1) + sumdiv(n, d, v[d])); v} \\ Andrew Howroyd, Aug 19 2018

CROSSREFS

Cf. A001678, A003238, A052409, A052410, A067824, A167865, A168532, A214577, A289078, A294336, A316782, A317099.

Sequence in context: A237351 A299490 A126471 * A199932 A305552 A226652

Adjacent sequences:  A317097 A317098 A317099 * A317101 A317102 A317103

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 01 2018

EXTENSIONS

Terms a(21) and beyond from Andrew Howroyd, Aug 19 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 4 08:18 EDT 2020. Contains 334825 sequences. (Running on oeis4.)