A137466 - OEIS

%I #16 Jun 13 2015 00:52:34

%S 1,121,12121,1212121,121212121,12121212121,1212121212121,

%T 121212121212121,12121212121212121,1212121212121212121,

%U 121212121212121212121,12121212121212121212121,1212121212121212121212121,121212121212121212121212121,12121212121212121212121212121

%N 1 concatenated with n 21's.

%H Vincenzo Librandi, <a href="/A137466/b137466.txt">Table of n, a(n) for n = 0..100</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).

%F From _Colin Barker_, May 31 2015: (Start)

%F   a(n) = (2^(3+2*n)*5^(1+2*n)-7)/33.

%F   a(n) = 100*a(n-1) + 21.

%F   a(n) = 101*a(n-1) - 100*a(n-2).

%F   G.f.: (20*x+1) / ((x-1)*(100*x-1)).

%F (End)

%e a(7) = 1 21 21 21 21 21 21 21.

%t Table[FromDigits[PadRight[{1},n,{1,2}]],{n,1,31,2}] (* or *) LinearRecurrence[{101,-100},{1,121},30] (* _Harvey P. Dale_, Aug 17 2013 *)

%o (PARI) Vec((20*x+1)/((x-1)*(100*x-1)) + O(x^30)) \\ _Colin Barker_, May 31 2015

%K easy,nonn,base

%O 0,2

%A _Ctibor O. Zizka_, Apr 19 2008

%E More terms from _Harvey P. Dale_, Aug 17 2013