A133472 a(n) = 10^n + 5.

6, 15, 105, 1005, 10005, 100005, 1000005, 10000005, 100000005, 1000000005, 10000000005, 100000000005, 1000000000005, 10000000000005, 100000000000005, 1000000000000005, 10000000000000005, 100000000000000005, 1000000000000000005, 10000000000000000005, 100000000000000000005

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Formula

From R. J. Mathar, Nov 30 2007: (Start)

O.g.f.: -3*(-2+17*x)/((-1+x)*(-1+10*x)) = -5/(-1+x) - 1/(-1+10*x).

a(n) = 10*a(n-1) - 45. (End)

a(n) = 10^n + 5. - Vincenzo Librandi, Aug 10 2011

From Elmo R. Oliveira, Jun 09 2025: (Start)

E.g.f.: exp(x)*(5 + exp(9*x)).

a(n) = 11*a(n-1) - 10*a(n-2).

a(n) = 3*A133473(n). (End)

Mathematica

Join[{6}, Table[10*FromDigits[PadRight[{1}, n, 0]]+5, {n, 20}]] (* or *) LinearRecurrence[{11, -10}, {6, 15}, 20] (* Harvey P. Dale, Sep 06 2020 *)

Prog

(Magma) [10^n+5: n in [0..20]]; // Vincenzo Librandi, Aug 10 2011
(PARI) apply( {A133472(n)=10^n+5}, [0..20]) \\ M. F. Hasler, Jun 15 2025

Crossrefs

Cf. A068128, A133384, A133473.

Sequence in context: A068128 A013222 A013228 * A213873 A372990 A219771

Adjacent sequences: A133469 A133470 A133471 * A133473 A133474 A133475

Keyword

nonn,easy

Author

Paul Curtz, Nov 29 2007

Extensions

Renamed by editors, Jun 16 2025

Status

approved