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A156641 a(n) = 13*(100^(n+1) - 1)/99.

%I A156641 #30 Sep 04 2024 18:55:18
%S A156641 13,1313,131313,13131313,1313131313,131313131313,13131313131313,
%T A156641 1313131313131313,131313131313131313,13131313131313131313,
%U A156641 1313131313131313131313,131313131313131313131313
%N A156641 a(n) = 13*(100^(n+1) - 1)/99.
%H A156641 Vincenzo Librandi, <a href="/A156641/b156641.txt">Table of n, a(n) for n = 0..100</a>
%H A156641 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).
%F A156641 G.f.: 13*x / ( (1-100*x)*(1-x) ).
%F A156641 a(n) = 13*A094028(n-1).
%F A156641 E.g.f.: (13/99)*(-exp(x) + 100*exp(100*x)). - _G. C. Greubel_, Feb 28 2021
%e A156641 For n=0, a(0)=13; n=1, a(1)=1313; n=2, a(2)=131313; n=3, a(3)=13131313.
%p A156641 A156641:= n-> (13/99)*(10^(2*n+2) -1); seq(A156641(n), n=0..15); # _G. C. Greubel_, Feb 28 2021
%t A156641 Table[FromDigits[PadLeft[{1,3},2n,{1,3}]],{n,15}] (* _Harvey P. Dale_, Jul 23 2011 *)
%o A156641 (Magma) [13*(100^(n+1)-1)/99: n in [0..15]];
%o A156641 (Sage) [(13/99)*(10^(2*n+2) -1) for n in (0..15)] # _G. C. Greubel_, Feb 28 2021
%o A156641 (PARI) a(n) = 100^(n+1)\99*13; \\ _Kevin Ryde_, Mar 05 2022
%Y A156641 Cf. A094028, A037582.
%K A156641 nonn,easy
%O A156641 0,1
%A A156641 _Vincenzo Librandi_, Feb 15 2009
%E A156641 Offset changed from 1 to 0