A156641 - OEIS

%I #30 Sep 04 2024 18:55:18

%S 13,1313,131313,13131313,1313131313,131313131313,13131313131313,

%T 1313131313131313,131313131313131313,13131313131313131313,

%U 1313131313131313131313,131313131313131313131313

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

%H Vincenzo Librandi, <a href="/A156641/b156641.txt">Table of n, a(n) for n = 0..100</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).

%F G.f.: 13*x / ( (1-100*x)*(1-x) ).

%F a(n) = 13*A094028(n-1).

%F E.g.f.: (13/99)*(-exp(x) + 100*exp(100*x)). - _G. C. Greubel_, Feb 28 2021

%e For n=0, a(0)=13; n=1, a(1)=1313; n=2, a(2)=131313; n=3, a(3)=13131313.

%p A156641:= n-> (13/99)*(10^(2*n+2) -1); seq(A156641(n), n=0..15); # _G. C. Greubel_, Feb 28 2021

%t Table[FromDigits[PadLeft[{1,3},2n,{1,3}]],{n,15}] (* _Harvey P. Dale_, Jul 23 2011 *)

%o (Magma) [13*(100^(n+1)-1)/99: n in [0..15]];

%o (Sage) [(13/99)*(10^(2*n+2) -1) for n in (0..15)] # _G. C. Greubel_, Feb 28 2021

%o (PARI) a(n) = 100^(n+1)\99*13; \\ _Kevin Ryde_, Mar 05 2022

%Y Cf. A094028, A037582.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Feb 15 2009

%E Offset changed from 1 to 0