cp's OEIS Frontend

A137739 Number of different strings of length n+6 obtained from "123...n" by iteratively duplicating any substring.

%I A137739 #17 Sep 26 2024 22:19:39
%S A137739 1,64,355,1014,2218,4217,7343,12018,18767,28233,41193,58575,81476,
%T A137739 111181,149183,197204,257217,331469,422505,533193,666750,826769,
%U A137739 1017247,1242614,1507763,1818081,2179481,2598435,3082008,3637893,4274447,5000728,5826533,6762437
%N A137739 Number of different strings of length n+6 obtained from "123...n" by iteratively duplicating any substring.
%C A137739 See A137743 for comments and examples.
%H A137739 <a href="/index/Do#repeat">Index entries for doubling substrings</a>
%H A137739 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A137739 a(n) = 1/720*(n+9)*(n^5+36*n^4+451*n^3+1716*n^2-380*n-8880)-1 for n>4.
%F A137739 G.f.: x*(x^10+3*x^9-6*x^8-26*x^7+221*x^5-370*x^4+162*x^3+72*x^2-57*x-1) / (x-1)^7. - _Colin Barker_, Nov 04 2013
%o A137739 (PARI) A137739(n)=if(n<2,1,n=A135473(n+6,n);n[ #n]) /* function A135473 defined in A137743 */
%o A137739 (PARI) A137739(n)=if(n>4,n*(n*(n*(n*(n*(n+45)+775)+5775)+15064)-12300)/6!-112,[1,64,355,1014][n])
%Y A137739 Cf. A137740-A137743, A135473, A137744-A137748.
%K A137739 nonn,easy
%O A137739 1,2
%A A137739 _M. F. Hasler_, Feb 10 2008
%E A137739 More terms from _Colin Barker_, Nov 04 2013