A093136 - OEIS

%I #32 May 08 2023 02:24:27

%S 1,2,20,200,2000,20000,200000,2000000,20000000,200000000,2000000000,

%T 20000000000,200000000000,2000000000000,20000000000000,

%U 200000000000000,2000000000000000,20000000000000000,200000000000000000,2000000000000000000,20000000000000000000

%N Expansion of (1 - 8*x)/(1 - 10*x).

%C A convex combination of 10^n and 0^n.

%C Inverse binomial transform of A083294. - _Stefano Spezia_, Jul 07 2021

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (10).

%F a(n) = (2*10^n + 8*0^n)/10.

%F a(n) = 2*10^(n-1), n > 0. - _Vincenzo Librandi_, Aug 02 2010

%F E.g.f.: (8 + 2*exp(10*x))/10. - _Stefano Spezia_, Jul 05 2021

%F From _Amiram Eldar_, May 08 2023: (Start)

%F Sum_{n>=0} 1/a(n) = 14/9.

%F Sum_{n>=0} (-1)^n/a(n) = 6/11.

%F Product_{n>=1} (1 - 1/a(n)) = A132026. (End)

%t CoefficientList[Series[(1-8x)/(1-10x),{x,0,30}],x] (* or *) LinearRecurrence[{10},{1,2},30] (* _Harvey P. Dale_, Oct 02 2022 *)

%o (PARI) Vec((1-8*x)/(1-10*x) + O(x^20)) \\ _Felix Fröhlich_, Jul 07 2021

%Y Partial sums are A093135.

%Y Cf. A083294, A132026.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 24 2004