A154549 a(n) = 111111*n.

111111, 222222, 333333, 444444, 555555, 666666, 777777, 888888, 999999, 1111110, 1222221, 1333332, 1444443, 1555554, 1666665, 1777776, 1888887, 1999998, 2111109, 2222220, 2333331, 2444442, 2555553, 2666664, 2777775, 2888886, 2999997, 3111108, 3222219, 3333330, 3444441, 3555552

Offset: 1

Author

Vincenzo Librandi, Jan 11 2009

Keywords

• nonn
• easy

Comments

This sequence was described by Magnitsky, Leontiy Filippovich (1669-1739), author of "The Russian Mathematical Encyclopedia" (1703) and other books. See the Kvant link. Magnitsky wrote it as a(n) = 143n*777. - Oleg Zyakun, Feb 28 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• A. Zhukov, Wonderful sequences, Kvant 6, 1998. (in Russian)
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Programs

Mathematica

LinearRecurrence[{2, -1}, {111111, 222222}, 20] (* Vincenzo Librandi, Feb 28 2012 *)
111111Range[30] (* Harvey P. Dale, Aug 11 2016 *)

PARI

a(n)=111111*n \\ Charles R Greathouse IV, Jan 11 2012

Formula

G.f.: 111111*x/(1-x)^2. - Vincenzo Librandi, Feb 29 2012

From Elmo R. Oliveira, Sep 15 2024: (Start)

E.g.f.: 111111*x*exp(x).

a(n) = a(n-1) + 111111 for n > 1.

a(n) = 2*a(n-1) - a(n-2) for n > 2. (End)