A185123 a(n) = n 9's sandwiched between two 1's.

11, 191, 1991, 19991, 199991, 1999991, 19999991, 199999991, 1999999991, 19999999991, 199999999991, 1999999999991, 19999999999991, 199999999999991, 1999999999999991, 19999999999999991, 199999999999999991, 1999999999999999991, 19999999999999999991

Offset: 0

Author

José María Grau Ribas, Jan 20 2012

Keywords

• nonn
• easy
• less
• base

Links

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

Crossrefs

Cf.A132583

Programs

Mathematica

H[n_]:=10^n+1+Sum[10^i*9,{i,1,n-1}];Array[H,100]
CoefficientList[Series[(11 + 70*x)/( (1-x)*(1-10*x) ), {x,0,50}], x] (* G. C. Greubel, Jun 23 2017 *)
Table[10FromDigits[PadRight[{1},n,9]]+1,{n,20}] (* or *) LinearRecurrence[ {11,-10},{11,191},20] (* Harvey P. Dale, May 18 2021 *)

PARI

a(n)=20*10^n-9 \\ Charles R Greathouse IV, Jan 20 2012

Formula

a(n) = 20*10^n - 9. - Charles R Greathouse IV, Jan 20 2012

a(0)=11, a(n) = 10*a(n-1) + 81.

From G. C. Greubel, Jun 22 2017: (Start)

G.f.: (11 + 70*x)/( (1-x)*(1-10*x) ).

E.g.f.: 20*exp(10*x) - 9*exp(x). (End)