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%I #18 Jul 12 2017 08:38:23
%S 2,1,5,5,12,16,30,45,77,121,200,320,522,841,1365,2205,3572,5776,9350,
%T 15125,24477,39601,64080,103680,167762,271441,439205,710645,1149852,
%U 1860496,3010350,4870845,7881197,12752041,20633240,33385280,54018522
%N a(n) = Lucas(n+1) + (3*(-1)^n - 1)/2.
%H Colin Barker, <a href="/A074392/b074392.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-1)
%F a(n) = Sum (L(2i+e), (i=0, 1, .., Floor(n/2))), where L(n) are Lucas numbers and e=2(n/2 - Floor(n/2)).
%F Convolution of L(n) with the sequence (1, 0, 1, 0, 1, 0, ...)
%F a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n>3.
%F G.f.: ( 2-x ) / ( (x-1)*(1+x)*(x^2+x-1) ).
%F a(n) = 2*A052952(n)-A052952(n-1). - _R. J. Mathar_, Oct 04 2013
%F a(n) = 2^(-1-n) * (3*(-2)^n - 2^n + (1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n)). - _Colin Barker_, Jul 12 2017
%t CoefficientList[Series[(2-x)/(1-x-2*x^2+x^3+x^4), {x, 0, 40}], x]
%o (PARI) Vec((2-x) / ((x-1)*(1+x)*(x^2+x-1)) + O(x^50)) \\ _Colin Barker_, Jul 12 2017
%Y Cf. A000032, A074331.
%Y Cf. A004146.
%K nonn,easy
%O 0,1
%A Mario Catalani (mario.catalani(AT)unito.it), Aug 22 2002
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