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%I #24 Feb 25 2017 02:48:05
%S 1,2,6,16,42,108,274,688,1714,4244,10458,25672,62826,153372,373666,
%T 908896,2207842,5357348,12988074,31464568,76179354,184347564,
%U 445923058,1078290832,2606699026,6300077492,15223631226,36780894376,88852528842,214620169788
%N Binomial transform of A052551.
%H G. C. Greubel, <a href="/A156664/b156664.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-2).
%F A007318 * A052551, where A052551 = (1, 1, 3, 3, 7, 7, 15, 15,...).
%F G.f.: (x^2 - 2*x + 1)/(2*x^3 + 3*x^2 - 4*x + 1). [_Alexander R. Povolotsky_, Feb 15 2009]
%F a(n) = 2*A000129(n+1)-2^n. [_R. J. Mathar_, Jun 15 2009]
%F a(n) = -2^n + (1-1/sqrt(2))*(1-sqrt(2))^n + (1+1/sqrt(2))*(1+sqrt(2))^n. - _Alexander R. Povolotsky_, Aug 16 2012
%F a(n+3) = -2*a(n) - 3*a(n+1) + 4*a(n+2). - _Alexander R. Povolotsky_, Aug 16 2012
%e a(3) = 16 = (1, 3, 3, 1) dot (1, 1, 3, 3) = (1 + 3 + 9 + 3).
%t CoefficientList[Series[(x^2-2x+1)/(2x^3+3x^2-4x+1),{x,0,40}],x] (* or *) LinearRecurrence[{4,-3,-2},{1,2,6},40] (* _Harvey P. Dale_, Apr 20 2013 *)
%o (PARI) x='x+O('x^50); Vec((x^2-2*x+1)/(2*x^3+3*x^2-4*x+1)) \\ _G. C. Greubel_, Feb 24 2017
%Y Cf. A052551
%K nonn,easy
%O 0,2
%A _Gary W. Adamson_, Feb 12 2009
%E Corrected and extended by _Harvey P. Dale_, Apr 20 2013
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