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

13, 1313, 131313, 13131313, 1313131313, 131313131313, 13131313131313, 1313131313131313, 131313131313131313, 13131313131313131313, 1313131313131313131313, 131313131313131313131313

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (101,-100).

Formula

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

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

E.g.f.: (13/99)*(-exp(x) + 100*exp(100*x)). - G. C. Greubel, Feb 28 2021

Example

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

Maple

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

Mathematica

Table[FromDigits[PadLeft[{1, 3}, 2n, {1, 3}]], {n, 15}] (* Harvey P. Dale, Jul 23 2011 *)

Prog

(Magma) [13*(100^(n+1)-1)/99: n in [0..15]]
(Sage) [(13/99)*(10^(2*n+2) -1) for n in (0..15)] # G. C. Greubel, Feb 28 2021
(PARI) a(n) = 100^(n+1)\99*13; \\ Kevin Ryde, Mar 05 2022

Crossrefs

Cf. A094028, A037582.

Sequence in context: A220619 A178560 A091781 * A300592 A221690 A197630

Adjacent sequences: A156638 A156639 A156640 * A156642 A156643 A156644

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 15 2009

Extensions

Offset changed from 1 to 0

Status

approved