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%I #9 Jun 30 2023 15:33:04
%S 279,3996,16008,64784,260640,1045568,4188288,16765184,67084800,
%T 268387328,1073645568,4294774784,17179484160,68718706688,274876366848,
%U 1099508547584,4398040350720,17592173723648,70368719536128
%N a(n) = 6*a(n-1)-8*a(n-2) for n > 3; a(0)=279, a(1)=3996, a(2)=16008, a(3)=64784.
%C Related to Reverse and Add trajectory of 775 in base 2: a(n) = A077077(4*n+1)/6, i.e. one sixth of second quadrisection of A077077.
%H Vincenzo Librandi, <a href="/A177844/b177844.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -8).
%F a(n) = 4^(n+5)-47*2^(n+1) for n > 1.
%F G.f.: (279+2322*x-5736*x^2+704*x^3) / ((1-2*x)*(1-4*x)).
%F G.f. for the sequence starting at a(2): 8*x^2*(2001-3908*x)/((1-2*x)*(1-4*x)).
%t CoefficientList[Series[(279 + 2322 x - 5736 x^2 + 704 x^3)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)
%o (PARI) {m=19; v=concat([279, 3996, 16008, 64784], vector(m-4)); for(n=5, m, v[n]=6*v[n-1]-8*v[n-2]); v}
%o (Magma) [279, 3996] cat [4^(n+5)-47*2^(n+1): n in [2..25]]; // _Vincenzo Librandi_, Sep 24 2013
%Y Cf. A077077 (Reverse and Add trajectory of 775 in base 2), A177843, A177845, A177846.
%K nonn,easy
%O 0,1
%A _Klaus Brockhaus_, May 14 2010
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