A205085 a(n) = n 5's sandwiched between two 1's.

11, 151, 1551, 15551, 155551, 1555551, 15555551, 155555551, 1555555551, 15555555551, 155555555551, 1555555555551, 15555555555551, 155555555555551, 1555555555555551, 15555555555555551, 155555555555555551, 1555555555555555551, 15555555555555555551, 155555555555555555551

Offset: 0

Author

José María Grau Ribas, Jan 22 2012

Keywords

• nonn
• base
• easy
• less

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. A002279.

Programs

Magma

I:=[11, 151]; [n le 2 select I[n] else 11*Self(n-1)-10*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Jan 23 2012

Mathematica

a[0]=11;a[n_]:=a[n-1]*10+41;Table[a[n],{n,0,44}]
LinearRecurrence[{11, -10}, {11, 151}, 50] (* Vincenzo Librandi, Jan 23 2012 *)
Table[10FromDigits[PadRight[{1},n,5]]+1,{n,20}] (* Harvey P. Dale, May 02 2019 *)

PARI

a(n)=(140*10^n-41)/9 \\ Charles R Greathouse IV, Jan 23 2012

Formula

a(0)=11, a(n) = 10*a(n-1) + 41.

a(n) = (140*10^n - 41)/9 (see PARI code by Charles R Greathouse IV).

a(n) = 11*a(n-1) - 10*a(n-2). - Vincenzo Librandi, Jan 23 2012

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

G.f.: (11 + 30*x)/((1 - x)*(1 - 10*x)).

E.g.f.: exp(x)*(140*exp(9*x) - 41)/9. (End)