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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A229900 G.f. satisfies: A(x) = x*exp( Sum_{n>=1} A(Lucas(n)*x^n) / n ). 2
1, 1, 3, 7, 22, 54, 192, 496, 1722, 4799, 17013, 48362, 169458, 498733, 1776570, 5331037, 18608396, 57109292, 201213331, 625146398, 2176243724, 6873338754, 24052502138, 76626395556, 265774736523, 856909651252, 2979519037203, 9675077715466, 33455355338926, 109591055905415 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Compare to: G(x) = x*exp( Sum_{n>=1} G(x^n)/n ), which is the g.f. of A000081, the number of rooted trees with n nodes.

Compare to: exp( Sum_{n>=1} Lucas(n)*x^n/n ) = 1/(1-x-x^2), which is the g.f. of the Fibonacci numbers.

The limit a(n+1)/a(n) seems to exist (near 3.5...); is this true?

LINKS

Table of n, a(n) for n=1..30.

EXAMPLE

G.f.: A(x) = x + x^2 + 3*x^3 + 7*x^4 + 22*x^5 + 54*x^6 + 192*x^7 + 496*x^8 +...

where

A(x) = x*exp(A(x) + A(3*x^2)/2 + A(4*x^3)/3 + A(7*x^4)/4 + A(11*x^5)/5 + A(18*x^6)/6 + A(29*x^7)/7 + A(47*x^8)/8 + A(76*x^9)/9 + A(123*x^10)/10 +...).

PROG

(PARI) {Lucas(n)=fibonacci(n-1)+fibonacci(n+1)}

{a(n)=local(A=x); for(i=1, n, A=x*exp(sum(k=1, n, subst(A, x, Lucas(k)*x^k +x*O(x^n))/k))); polcoeff(A, n)}

for(n=1, 30, print1(a(n), ", "))

CROSSREFS

Cf. A000032 (Lucas), A229807, A229901.

Sequence in context: A182174 A080882 A229807 * A079120 A092566 A036719

Adjacent sequences:  A229897 A229898 A229899 * A229901 A229902 A229903

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 02 2013

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 May 26 02:35 EDT 2019. Contains 323579 sequences. (Running on oeis4.)