A173735 a(n) = (10^n + 26)/9.

3, 4, 14, 114, 1114, 11114, 111114, 1111114, 11111114, 111111114, 1111111114, 11111111114, 111111111114, 1111111111114, 11111111111114, 111111111111114, 1111111111111114, 11111111111111114, 111111111111111114, 1111111111111111114, 11111111111111111114, 111111111111111111114

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100 (term 0 added by Ivan Panchenko)

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

Formula

a(n) = a(n-1) + 10^(n-1) = 10*a(n-1) - 26, a(0)=3.

a(n) = 11*a(n-1) - 10*a(n-2). - Vincenzo Librandi, Jul 05 2012

a(n) = 2*(A002279(n-1) + 2). - Martin Ettl, Nov 12 2012

G.f.: (3-29*x)/((1-x)*(1-10*x)). - Ivan Panchenko, Nov 05 2013

From Elmo R. Oliveira, Jun 18 2025: (Start)

E.g.f.: exp(x)*(26 + exp(9*x))/9.

a(n) = 2*A178769(n-1) for n >= 1. (End)

Mathematica

CoefficientList[Series[(3-29*x)/((1-x)*(1-10*x)), {x, 0, 30}], x] (* Ivan Panchenko, Nov 05 2013 *)
LinearRecurrence[{11, -10}, {3, 4}, 30] (* Harvey P. Dale, Apr 09 2026 *)

Prog

(Magma) [(10^n+26)/9: n in [0..20]]; // Ivan Panchenko, Nov 05 2013
(Maxima) A173735(n):=(10^n+26)/9$
makelist(A173735(n), n, 0, 20); /* Ivan Panchenko, Nov 03 2013 */

Crossrefs

Cf. A002279, A178769.

Sequence in context: A176857 A356463 A248152 * A368456 A286705 A286081

Adjacent sequences: A173732 A173733 A173734 * A173736 A173737 A173738

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 23 2010

Extensions

a(0) from Ivan Panchenko, Nov 05 2013

Status

approved