A165246 a(n) = (10^n + 53)/9.

7, 17, 117, 1117, 11117, 111117, 1111117, 11111117, 111111117, 1111111117, 11111111117, 111111111117, 1111111111117, 11111111111117, 111111111111117, 1111111111111117, 11111111111111117, 111111111111111117, 1111111111111111117, 11111111111111111117, 111111111111111111117

Offset: 1

Author

Ivan Panchenko, Sep 10 2009

Keywords

• nonn
• easy

Comments

a(n) are also n-1 units followed by a seven.

Links

• Markus Tervooren, Factorizations of (1)w7.
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Programs

Mathematica

Table[FromDigits[PadLeft[{7}, n, 1]], {n, 20}] (* Harvey P. Dale, Oct 17 2011 *)

PARI

my(x='x+O('x^22)); Vec(x*(7-60*x)/((1-11*x+10*x^2))) \\ Elmo R. Oliveira, Jun 17 2025

Formula

a(n) = 9*a(n-1) - 8*a(n-2) + 2*10^(n-2) for n>2, a(1)=7, a(2)=17. - Vincenzo Librandi, Aug 02 2010

From Colin Barker, Jan 24 2013: (Start)

a(n) = 11*a(n-1) - 10*a(n-2).

G.f.: -x*(60*x-7)/((x-1)*(10*x-1)). (End)

E.g.f.: -6 + exp(x)*(53 + exp(9*x))/9. - Elmo R. Oliveira, Jun 17 2025

Extensions

More terms from Elmo R. Oliveira, Jun 17 2025