%I A097417
%S A097417 1,1,2,5,13,34,90,236,621,1629,4274,11193,29337,76818,201173,526730,
%T A097417 1379178,3610804,9453695,24750281,64798235,169644626,444138288,
%U A097417 1162770238,3044180080,7969770106,20865148382,54625676431,143011928942
%N A097417 a(1)=1; a(n+1) = sum{k=1 to n} a(k) a(floor(n/k)).
%C A097417 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 (mymontain(AT)yahoo.com), Feb 05 2005
%H A097417 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%F A097417 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
%F A097417 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 ->infty a(n)/(1+Phi)^n exists but should not have a simple 
               closed form. - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 29 
               2004
%p A097417 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) (from Mark Hudson)
%t A097417 a[1] = 1; a[n_] := a[n] = Sum[ a[k]*a[Floor[(n - 1)/k]], {k, n - 1}]; 
               Table[ a[n], {n, 29}] (from Robert G. Wilson v Aug 21 2004)
%o A097417 (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
%Y A097417 Cf. A097919, A038044, A078346.
%Y A097417 Sequence in context: A099496 A114299 A112842 this_sequence A006801 A114173 
               A023425
%Y A097417 Adjacent sequences: A097414 A097415 A097416 this_sequence A097418 A097419 
               A097420
%K A097417 easy,nonn
%O A097417 1,3
%A A097417 Leroy Quet Aug 19 2004
%E A097417 More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Robert 
               G. Wilson v (rgwv(AT)rgwv.com) and Mark Hudson (mrmarkhudson(AT)hotmail.com), 
               Aug 21 2004