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A137739 Number of different strings of length n+6 obtained from "123...n" by iteratively duplicating any substring. 4

%I

%S 1,64,355,1014,2218,4217,7343,12018,18767,28233,41193,58575,81476,

%T 111181,149183,197204,257217,331469,422505,533193,666750,826769,

%U 1017247,1242614,1507763,1818081,2179481,2598435,3082008,3637893,4274447,5000728,5826533,6762437

%N Number of different strings of length n+6 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>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F 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 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 (PARI) A137739(n)=if(n<2,1,n=A135473(n+6,n);n[ #n]) /* function A135473 defined in A137743 */

%o (PARI) A137739(n)=if(n>4,n*(n*(n*(n*(n+45)+775)+5775)+15064)-12300)/7!-112,[1,64,355,1014][n])

%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

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Last modified July 23 12:19 EDT 2021. Contains 346259 sequences. (Running on oeis4.)