The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A097417 a(1)=1; a(n+1) = Sum_{k=1..n} a(k) a(floor(n/k)). 2
 1, 1, 2, 5, 13, 34, 90, 236, 621, 1629, 4274, 11193, 29337, 76818, 201173, 526730, 1379178, 3610804, 9453695, 24750281, 64798235, 169644626, 444138288, 1162770238, 3044180080, 7969770106, 20865148382, 54625676431, 143011928942 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 4 is the only composite number n such that a(n+1) = 3a(n) - a(n-1) and if n is a composite number greater than 4 then a(n+1) > 3a(n) - a(n-1). - Farideh Firoozbakht, Feb 05 2005 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 FORMULA Ratio a(n+1)/a(n) seems to tend to 1 + Golden Ratio = 2.61803398... = 1 + A001622. - Mark Hudson (mrmarkhudson(AT)hotmail.com), Aug 23 2004 Satisfies the "partial linear recursion": a(prime(n)+1) = 3*a(prime(n)) - a(prime(n)-1). This explains why we get a(n+1)/a(n) -> 1 + phi. Also, lim_{n->oo} a(n)/(1 + phi)^n exists but should not have a simple closed form. - Benoit Cloitre, Aug 29 2004 Limit_{n->oo} a(n)/(1 + phi)^n = 0.108165624886204570982244311730754895284041534583990405146651275318889227986... - Vaclav Kotesovec, May 28 2021 MAPLE a[1]:=1: for n from 1 to 50 do: a[n+1]:=sum(a[k]*a[floor(n/k)], k=1..n): od: seq(a[i], i=1..51) # Mark Hudson, Aug 21 2004 MATHEMATICA a[1] = 1; a[n_] := a[n] = Sum[ a[k]*a[Floor[(n - 1)/k]], {k, n - 1}]; Table[ a[n], {n, 29}] (* Robert G. Wilson v, Aug 21 2004 *) PROG (PARI) {m=29; a=vector(m); print1(a[1]=1, ", "); for(n=1, m-1, print1(a[n+1]=sum(k=1, n, a[k]*a[floor(n/k)]), ", "))} \\ Klaus Brockhaus, Aug 21 2004 CROSSREFS Cf. A038044, A078346, A097919. Sequence in context: A367658 A114299 A112842 * A367657 A006801 A329674 Adjacent sequences: A097414 A097415 A097416 * A097418 A097419 A097420 KEYWORD easy,nonn AUTHOR Leroy Quet, Aug 19 2004 EXTENSIONS More terms from Klaus Brockhaus, Robert G. Wilson v and Mark Hudson (mrmarkhudson(AT)hotmail.com), Aug 21 2004 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 May 28 21:13 EDT 2024. Contains 372920 sequences. (Running on oeis4.)