1,2

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.

Index entries for doubling substrings

(PARI) A137742(n)=if(n<2, 1, n=A135473(n+3, n); n[ #n]) /* function A135473 defined in A137743 */

(PARI) A137742(n)=if(n<2, 1, (n - 1)*(n + 4)*(n + 6)/6)

Cf. A137740-A137743, A135473, A137744-A137748.

Sequence in context: A154894 A000567 A124484 this_sequence A152117 A075629 A067334

Adjacent sequences: A137739 A137740 A137741 this_sequence A137743 A137744 A137745

nonn

M. F. Hasler (MHasler(AT)univ-ag.fr), Feb 10 2008