The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A171213 G.f.: A(x) = x + x*A(A(3x)). 2
 1, 3, 54, 3402, 618921, 318392208, 474852630879, 2094575471899362, 27570620677894020891, 1086589159409074932937593, 128377839432663886566934695744, 45490432595875817814676362194769627 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS More generally, if F(x) = x + x*F(F(qx)), then F(x) = x + x*F(qx) + x*F(qx)*F(qF(qx) + x*F(qx)*F(qF(qx))*F(qF(qF(qx))) +... with a simple solution at q=1/2: F(x) = x/(1-x/2) satisfies: F(x) = x + x*F(F(x/2)). LINKS Table of n, a(n) for n=1..12. EXAMPLE G.f.: A(x) = x + 3*x^2 + 54*x^3 + 3402*x^4 + 618921*x^5 +... A(A(x)) = x + 6*x^2 + 126*x^3 + 7641*x^4 + 1310256*x^5 +...+ a(n)*x^n/3^(n-1) +... As a formal series involving products of iterations of the g.f., A(x) = x + x*A(3x) + x*A(3x)*A(3A(3x) + x*A(3x)*A(3A(3x))*A(3A(3A(3x))) +... which, upon replacing x with A(3x), yields: A(A(3x)) = A(3x) + A(3x)*A(3A(3x)) + A(3x)*A(3A(3x))*A(3A(3A(3x))) +... thus A(x) = x + x*A(A(3x)). PROG (PARI) {a(n, q=3)=local(A=x+x^2); for(i=1, n, A=x+x*subst(A, x, subst(A, x, q*x+O(x^n)))); polcoeff(A, n)} CROSSREFS Cf. A171212 (q=2), A171214 (q=1/3). Sequence in context: A224368 A091826 A091796 * A006025 A049414 A003027 Adjacent sequences: A171210 A171211 A171212 * A171214 A171215 A171216 KEYWORD nonn AUTHOR Paul D. Hanna, Dec 08 2009 STATUS approved

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

Last modified December 10 22:38 EST 2023. Contains 367717 sequences. (Running on oeis4.)