A154549 - OEIS

%I #40 Sep 15 2024 14:32:57

%S 111111,222222,333333,444444,555555,666666,777777,888888,999999,

%T 1111110,1222221,1333332,1444443,1555554,1666665,1777776,1888887,

%U 1999998,2111109,2222220,2333331,2444442,2555553,2666664,2777775,2888886,2999997,3111108,3222219,3333330,3444441,3555552

%N a(n) = 111111*n.

%C 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

%H Vincenzo Librandi, <a href="/A154549/b154549.txt">Table of n, a(n) for n = 1..1000</a>

%H A. Zhukov, <a href="http://kvant.mccme.ru/pdf/1998/06/kv0698kaleid.pdf">Wonderful sequences</a>, Kvant 6, 1998. (in Russian)

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: 111111*x/(1-x)^2. - _Vincenzo Librandi_, Feb 29 2012

%F From _Elmo R. Oliveira_, Sep 15 2024: (Start)

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

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

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

%t LinearRecurrence[{2, -1}, {111111, 222222}, 20] (* _Vincenzo Librandi_, Feb 28 2012 *)

%t 111111Range[30] (* _Harvey P. Dale_, Aug 11 2016 *)

%o (PARI) a(n)=111111*n \\ _Charles R Greathouse IV_, Jan 11 2012

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Jan 11 2009