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%I #32 Feb 09 2024 11:15:51
%S 5,19,68,268,1040,4144,16448,65728,262400,1049344,4195328,16780288,
%T 67112960,268447744,1073758208,4295016448,17179934720,68719673344,
%U 274878169088,1099512414208,4398047559680,17592189190144,70368748371968,281474989293568,1125899923619840
%N a(n) = 2^(n-2)*(2^(n+4)-(-1)^n+5).
%H Vincenzo Librandi, <a href="/A240525/b240525.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,4,-16).
%F G.f.: (5-x-28*x^2)/(1-4*x-4*x^2+16*x^3).
%F a(n) = 4*a(n-1) + 4*a(n-2)- 16*a(n-3) with n>2, a(0)=5, a(1)=19, a(2)=68.
%F a(n) = (5*2^n-(-2)^n)/4+4^(n+1) = A084221(n)+A000302(n+1).
%t CoefficientList[Series[(5 - x - 28 x^2)/(1 - 4 x - 4 x^2 + 16 x^3), {x, 0, 33}], x]
%o (Magma) [2^(n-2)*(2^(n+4)-(-1)^n+5): n in [0..25]] /* or */ I:=[5,19,68]; [n le 3 select I[n] else 4*Self(n-1)+4*Self(n-2)-16*Self(n-3): n in [1..30]]
%o (PARI) a(n)=(2^(n+4)-(-1)^n+5)<<(n-2) \\ _Charles R Greathouse IV_, Aug 26 2014
%Y Cf. A000302, A084221.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Apr 07 2014
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