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%I #20 Sep 08 2022 08:45:09
%S 1,7,58,532,5128,50512,502048,5008192,50032768,500131072,5000524288,
%T 50002097152,500008388608,5000033554432,50000134217728,
%U 500000536870912,5000002147483648,50000008589934592,500000034359738368
%N a(n) = (10^n + 4^n)/2.
%C Binomial transform of A025551. 7th binomial transform of {1, 0, 9, 0, 81, 0, 729, 0, ...}.
%H Vincenzo Librandi, <a href="/A081343/b081343.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 (14,-40).
%F a(n) = 14*a(n-1) -40*a(n-2), a(0)=1, a(1)=7.
%F G.f.: (1-7*x)/((1-4*x)*(1-10*x)).
%F E.g.f.: exp(7*x) * cosh(3*x).
%F a(n) = ((7+sqrt(9))^n + (7-sqrt(9))^n)/2. - Al Hakanson (hawkuu(AT)gmail.com), Dec 08 2008
%p seq( (10^n + 4^n)/2, n=0..25); # _G. C. Greubel_, Jan 07 2020
%t CoefficientList[Series[(1-7x)/((1-4x)(1-10x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Aug 08 2013 *)
%o (Magma) [(10^n+4^n)/2: n in [0..25]]; // _Vincenzo Librandi_, Aug 08 2013
%o (PARI) a(n)=(10^n+4^n)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Sage) [(10^n + 4^n)/2 for n in (0..25)] # _G. C. Greubel_, Jan 07 2020
%o (GAP) List([0..25], n-> (10^n + 4^n)/2); # _G. C. Greubel_, Jan 07 2020
%Y Cf. A081342.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 18 2003
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