A133472 - OEIS

%I #24 Feb 27 2024 03:02:19

%S 6,15,105,1005,10005,100005,1000005,10000005,100000005,1000000005,

%T 10000000005,100000000005,1000000000005,10000000000005,

%U 100000000000005,1000000000000005,10000000000000005,100000000000000005

%N 6 followed by numbers with n-1 0's between 1 and 5.

%H Vincenzo Librandi, <a href="/A133472/b133472.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).

%F From _R. J. Mathar_, Nov 30 2007: (Start)

%F O.g.f.: -3*(-2+17*x)/((-1+x)*(-1+10*x)) = -5/(-1+x) - 1/(-1+10*x).

%F a(n) = 10*a(n-1) - 45. (End)

%F a(n) = 10^n + 5. - _Vincenzo Librandi_, Aug 10 2011

%t Join[{6},Table[10*FromDigits[PadRight[{1},n,0]]+5,{n,20}]] (* or *) LinearRecurrence[{11,-10},{6,15},20] (* _Harvey P. Dale_, Sep 06 2020 *)

%o (Magma) [10^n+5: n in [0..20]]; // _Vincenzo Librandi_, Aug 10 2011

%Y Cf. A068128, A133384.

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Nov 29 2007