login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A029857 Number of rooted trees with 3-colored leaves. 4
3, 3, 9, 28, 94, 328, 1197, 4486, 17235, 67429, 267932, 1078003, 4383784, 17987897, 74385984, 309694232, 1297037177, 5460726214, 23098296648, 98113995068, 418335662448, 1789814398035, 7681522429474, 33061825858259, 142674028869587, 617180102839217 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..500

Index entries for sequences related to rooted trees

N. J. A. Sloane, Transforms

FORMULA

Shifts left under Euler transform.

a(n) ~ c * d^n / n^(3/2), where d = 4.58859196701042554480382685... and c = 0.5102557157321640697473838... - Vaclav Kotesovec, Mar 29 2014

MAPLE

with(numtheory): a:= proc(n) option remember; local d, j; if n<=1 then 3*n else (add(d*a(d), d=divisors(n-1)) +add(add(d*a(d), d=divisors(j)) *a(n-j), j=1..n-2))/ (n-1) fi end: seq(a(n), n=1..30); # Alois P. Heinz, Sep 06 2008

MATHEMATICA

a[n_] := a[n] = If[n<=1, 3*n, (Sum[d*a[d], {d, Divisors[n-1]}] + Sum[Sum[ d*a[d], {d, Divisors[j]}]*a[n-j], {j, 1, n-2}])/(n-1)]; Table[a[n], {n, 1, 30}] (* Jean-Fran├žois Alcover, Feb 21 2016 *)

CROSSREFS

Cf. A000081, A029856, A038050.

Sequence in context: A229024 A117976 A010098 * A257611 A268617 A264412

Adjacent sequences:  A029854 A029855 A029856 * A029858 A029859 A029860

KEYWORD

nonn,easy,eigen

AUTHOR

Christian G. Bower

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 January 21 17:47 EST 2019. Contains 319349 sequences. (Running on oeis4.)