A173776 a(n) = (4*10^n + 41)/9.

5, 9, 49, 449, 4449, 44449, 444449, 4444449, 44444449, 444444449, 4444444449, 44444444449, 444444444449, 4444444444449, 44444444444449, 444444444444449, 4444444444444449, 44444444444444449, 444444444444444449

Offset: 0

Author

Vincenzo Librandi, Feb 24 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A093402.

Programs

Magma

[(4*10^n+41)/9: n in [0..20]]; // Vincenzo Librandi, Jul 05 2012

Mathematica

Join[{5}, FromDigits/@Table[PadLeft[{9}, n, 4], {n,20}]] (* or *) Join[{5}, NestList[10#-41&, 9, 20]] (* Harvey P. Dale, Feb 17 2012 *)
CoefficientList[Series[(5-46*x)/((1-x)*(1-10*x)),{x,0,30}],x] (* Vincenzo Librandi, Jul 05 2012 *)

Sage

[(4*10^n + 41)/9 for n in (0..30)] # G. C. Greubel, Jul 06 2021

Formula

a(n) = 10*a(n-1) - 41 with n>0, a(0)=5.

G.f.: (5 - 46*x)/((1-x)*(1-10*x)). - Vincenzo Librandi, Jul 05 2012

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

E.g.f.: (1/9)*(41*exp(x) + 4*exp(10*x)). - G. C. Greubel, Jul 06 2021