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%I #26 Sep 08 2022 08:45:09
%S 1,10,101,1030,10601,110050,1151501,12135070,128702801,1372684090,
%T 14712104501,158346365110,1710428956601,18532288986130,
%U 201313313019101,2191569650755150,23901375026212001,261062105099480170
%N 10th binomial transform of (1,0,1,0,1,......), A059841.
%C Binomial transform of A060531.
%C Average of binomial and inverse binomial transforms of 10^n.
%C a(n) is also the number of words of length n over an alphabet of eleven letters with a chosen letter appearing an even number of times. See a comment in A007582, also for the crossrefs. for the 1- to 10- letter word cases. - _Wolfdieter Lang_, Jul 17 2017
%H Vincenzo Librandi, <a href="/A081192/b081192.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-99).
%F a(n) = 20*a(n-1) -99*a(n-2), a(0)=1, a(1)=10.
%F G.f.: (1-10*x)/((1-9*x)*(1-11*x)).
%F E.g.f.: exp(10*x) * cosh(x).
%F a(n) = 9^n/2 + 11^n/2.
%F a(n) = Sum_{k=0..floor(n/2)} C(n,2*k)*10^(n-2*k).
%p A081192:=n->9^n/2 + 11^n/2: seq(A081192(n), n=0..30); # _Wesley Ivan Hurt_, May 03 2017
%t CoefficientList[Series[(1-10x)/((1-9x)(1-11x)),{x,0,200}],x] (* _Vincenzo Librandi_, Aug 07 2013 *)
%o (Magma) [9^n/2 + 11^n/2: n in [0..25]]; // _Vincenzo Librandi_, Aug 07 2013
%Y Cf. A007582, A059841, A060531.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 11 2003
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