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A081203 9th binomial transform of (0,1,0,1,0,1,.....), A000035.

%I A081203 #20 Sep 08 2022 08:45:09
%S A081203 0,1,18,244,2952,33616,368928,3951424,41611392,432891136,4463129088,
%T A081203 45705032704,465640261632,4725122093056,47800976744448,
%U A081203 482407813955584,4859262511644672,48874100093157376,490992800745259008
%N A081203 9th binomial transform of (0,1,0,1,0,1,.....), A000035.
%C A081203 Binomial transform of A081202.
%C A081203 From _Wolfdieter Lang_, Jul 17 2017: (Start)
%C A081203 For a combinatorial interpretation of a(n) with special 10-letter words of length n see the comment in A081200 on the 7-letter analog.
%C A081203 The binomial transform of {a(n)}_{n >= 0} is {0, A016190}, the 11-letter analog.
%C A081203 (End)
%H A081203 Vincenzo Librandi, <a href="/A081203/b081203.txt">Table of n, a(n) for n = 0..200</a>
%H A081203 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-80).
%F A081203 a(n) = 18*a(n-1)-80*a(n-2), a(0)=0, a(1)=1.
%F A081203 G.f.: x/((1-8*x)*(1-10*x)).
%F A081203 a(n) = 10^n/2 - 8^n/2.
%t A081203 CoefficientList[Series[x / ((1 - 8 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Aug 07 2013 *)
%t A081203 LinearRecurrence[{18,-80},{0,1},20] (* _Harvey P. Dale_, Aug 05 2018 *)
%o A081203 (Magma) [10^n/2 - 8^n/2: n in [0..25]]; // _Vincenzo Librandi_, Aug 07 2013
%Y A081203 Apart from the first term, identical to A016186.
%Y A081203 Cf. A000035, A016190, A081202, A081200, A081201, A081202.
%K A081203 easy,nonn
%O A081203 0,3
%A A081203 _Paul Barry_, Mar 11 2003