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%I #18 Jan 07 2023 18:48:39
%S 5,18,68,264,1040,4128,16448,65664,262400,1049088,4195328,16779264,
%T 67112960,268443648,1073758208,4295000064,17179934720,68719607808,
%U 274878169088,1099512152064,4398047559680,17592188141568,70368748371968,281474985099264
%N a(n) = 2^(2n) + 2^(n-1).
%C A bisection of A001445.
%C a(n) written in base 2: 101, 10010, 1000100, 100001000, ..., i.e. number 1, n times 0, number 1, (n-1) times 0 (see A164367). [_Jaroslav Krizek_, Aug 14 2009]
%H G. C. Greubel, <a href="/A164051/b164051.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-8).
%F a(n) = A001445(2n+1).
%F a(n) = 6*a(n-1) - 8*a(n-2).
%F G.f.: x*(5-12*x)/((1-4*x)*(1-2*x)).
%F E.g.f.: (-3 + exp(2*x) + 2*exp(4*x))/2. - _Ilya Gutkovskiy_, Jun 21 2016
%t Table[2^(2 n) + 2^(n - 1), {n, 24}] (* or *)
%t Rest@ CoefficientList[Series[-x (-5 + 12 x)/((4 x - 1) (2 x - 1)), {x, 0, 24}], x] (* _Michael De Vlieger_, Jun 21 2016 *)
%t LinearRecurrence[{6,-8},{5,18},30] (* _Harvey P. Dale_, Jan 07 2023 *)
%o (PARI) x='x+O('x^50); Vec(x*(5-12*x)/((1-4*x)*(1-2*x))) \\ _G. C. Greubel_, Sep 08 2017
%o (PARI) a(n) = 2^(2*n) + 2^(n-1); \\ _Michel Marcus_, Sep 09 2017
%K nonn,easy
%O 1,1
%A _Jaroslav Krizek_, Aug 08 2009
%E Edited and extended by _R. J. Mathar_, Aug 11 2009
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