A171553 a(n) = 9*10^n + 100^n + 1.

11, 191, 10901, 1009001, 100090001, 10000900001, 1000009000001, 100000090000001, 10000000900000001, 1000000009000000001, 100000000090000000001, 10000000000900000000001, 1000000000009000000000001, 100000000000090000000000001, 10000000000000900000000000001

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Formula

G.f.: -(1910*x^2-1030*x+11) / ((x-1)*(10*x-1)*(100*x-1)). - Colin Barker, Jul 29 2014

From Elmo R. Oliveira, Sep 06 2024: (Start)

E.g.f.: exp(x)*(9*exp(9*x) + exp(99*x) + 1).

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2. (End)

Mathematica

Join[{11}, Table[FromDigits[Join[{1}, PadRight[{}, n, 0], {9}, PadRight[{}, n, 0], {1}]], {n, 0, 20}]] (* Harvey P. Dale, Apr 26 2013 *)
Table[100^n + 9 * 10^n + 1, {n, 0, 19}] (* Alonso del Arte, Jul 28 2014 *)

Prog

(Magma) [1+9*10^n+100^n: n in [0..15]]; // Vincenzo Librandi, Jul 29 2014
(PARI) Vec(-(1910*x^2-1030*x+11)/((x-1)*(10*x-1)*(100*x-1)) + O(x^100)) \\ Colin Barker, Jul 29 2014

Crossrefs

Cf. A100459.

Sequence in context: A280070 A384136 A397241 * A333759 A068649 A158509

Adjacent sequences: A171550 A171551 A171552 * A171554 A171555 A171556

Keyword

easy,nonn

Author

Jason Earls, Dec 11 2009

Extensions

More terms from Harvey P. Dale, Apr 26 2013

Status

approved