A137741 - OEIS

%I #14 May 12 2017 02:55:30

%S 1,16,54,119,218,360,555,814,1149,1573,2100,2745,3524,4454,5553,6840,

%T 8335,10059,12034,14283,16830,19700,22919,26514,30513,34945,39840,

%U 45229,51144,57618,64685,72380,80739,89799,99598,110175,121570,133824,146979,161078

%N Number of different strings of length n+4 obtained from "123...n" by iteratively duplicating any substring.

%C See A137743 for comments and examples.

%H <a href="/index/Do#repeat">Index entries for doubling substrings</a>

%F a(n) = n^4 for n=1,2; a(n) = 1/24*(n+3)*(n^3+15*n^2+50*n-96) for n>2 (conjectured).

%F G.f.: x*(x^6+x^5-8*x^4+x^3+16*x^2-11*x-1) / (x-1)^5 (conjectured). - _Colin Barker_, Nov 04 2013

%o (PARI) A137741(n)=if(n<2,1,n=A135473(n+4,n);n[ #n]) /* function A135473 defined in A137743 */

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

%K nonn,easy

%O 1,2

%A _M. F. Hasler_, Feb 10 2008

%E More terms from _Colin Barker_, Nov 04 2013