%I A137742
%S A137742 1,8,21,40,66,100,143,196,260,336,425,528,646,780,931,1100,1288,1496,
%T A137742 1725,1976,2250,2548,2871,3220
%N A137742 a(n)=(n-1)(n+4)(n+6)/6 for n>1, a(1)=1.
%C A137742 Also the number of different strings of length n+3 obtained from "123...n" 
               by iteratively duplicating any substring (see A137743 for comments 
               and examples). This is the principal (although not simplest) definition 
               of this sequence and explains why a(1)=1 and not 0.
%H A137742 <a href="Sindx_Do.html#repeat">Index entries for doubling substrings</
               a>
%o A137742 (PARI) A137742(n)=if(n<2,1,n=A135473(n+3,n);n[ #n]) /* function A135473 
               defined in A137743 */
%o A137742 (PARI) A137742(n)=if(n<2,1,(n - 1)*(n + 4)*(n + 6)/6)
%Y A137742 Cf. A137740-A137743, A135473, A137744-A137748.
%Y A137742 Sequence in context: A154894 A000567 A124484 this_sequence A152117 A075629 
               A067334
%Y A137742 Adjacent sequences: A137739 A137740 A137741 this_sequence A137743 A137744 
               A137745
%K A137742 nonn
%O A137742 1,2
%A A137742 M. F. Hasler (MHasler(AT)univ-ag.fr), Feb 10 2008