A133384 Numbers with n 0's between 1 and 2.

12, 102, 1002, 10002, 100002, 1000002, 10000002, 100000002, 1000000002, 10000000002, 100000000002, 1000000000002, 10000000000002, 100000000000002, 1000000000000002, 10000000000000002, 100000000000000002, 1000000000000000002, 10000000000000000002

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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

Formula

a(n) = 10^(n+1) + 2. - Vincenzo Librandi, Aug 10 2011

a(n) = 11*a(n-1) - 10*a(n-2); a(0)=12, a(1)=102. - Harvey P. Dale, Oct 03 2013

From Stefano Spezia, Nov 30 2023: (Start)

O.g.f.: 6*(2 - 5*x)/((1 - x)*(1 - 10*x)).

E.g.f.: 2*exp(x)*(1 + 5*exp(9*x)).

(R(a(n)) + 1)/(a(n) - 1) = 2, where R(k) = A004086(k). (End)

a(n) = 6 * A126109(n). - Alois P. Heinz, Nov 30 2023

Mathematica

Table[FromDigits[Join[PadRight[{1}, n, 0], {2}]], {n, 20}] (* or *) 10^Range[20]+2 (* or *) LinearRecurrence[{11, -10}, {12, 102}, 20] (* Harvey P. Dale, Oct 03 2013 *)

Prog

(Magma) [10^(n+1)+2: n in [0..20]]; // Vincenzo Librandi, Aug 10 2011

Crossrefs

Subsequence of A052148.

Cf. A004086, A126109.

Sequence in context: A240462 A126533 A052148 * A052067 A307821 A050791

Adjacent sequences: A133381 A133382 A133383 * A133385 A133386 A133387

Keyword

nonn,base,easy

Author

Paul Curtz, Oct 29 2007

Status

approved