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

0,1

Links

Table of n, a(n) for n=0..18.

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

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)

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 *)

Prog

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

Crossrefs

Cf.A132583

Sequence in context: A034787 A001408 A298643 * A036936 A002195 A280070

Adjacent sequences: A185120 A185121 A185122 * A185124 A185125 A185126

Keyword

nonn,easy,less,base

Author

José María Grau Ribas, Jan 20 2012

Status

approved