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%I #30 Sep 08 2022 08:45:09
%S 1,5,29,185,1241,8525,59189,412865,2885681,20186645,141267149,
%T 988751945,6920909321,48445302365,339113927909,2373787929425,
%U 16616486808161,116315321563685,814206992665469,5699448173817305,39896134892198201
%N a(n) = (7^n + 3^n)/2.
%C Binomial transform of A081336.
%C 5th binomial transform of (1,0,4,0,16,0,64,...).
%H Vincenzo Librandi, <a href="/A081336/b081336.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 (10,-21).
%F a(n) = 10*a(n-1) - 21*a(n-2), a(0)=1, a(1)=5.
%F G.f.: (1-5*x)/((1-3*x)*(1-7*x)).
%F E.g.f.: exp(5*x) * cosh(2*x).
%F a(n) = A074608(n) / 2. - _Michel Marcus_, Oct 07 2015
%F a(n) = Sum_{k=0..n} A027907(n,2k)*4^k . - _J. Conrad_, Aug 24 2016
%t CoefficientList[Series[(1 - 5 x) / ((1 - 3 x) (1 - 7 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Aug 08 2013 *)
%t LinearRecurrence[{10,-21},{1,5},30] (* _Harvey P. Dale_, Dec 07 2014 *)
%o (Magma) [(7^n+3^n)/2: n in [0..25]]; // _Vincenzo Librandi_, Aug 08 2013
%o (PARI) a(n)=(7^n+3^n)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A074608, A081337.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Mar 18 2003
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