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%I #15 Jun 23 2018 02:32:30
%S 4,13,45,152,491,1531,4652,13865,40713,118144,339559,968183,2742100,
%T 7721797,21637221,60367976,167787107,464776435,1283571068,3535240289,
%U 9713031489,26627195728,72847698655,198929987567,542305383076,1476061431421
%N Bisection of A099924 (convolution of Lucas numbers); even arguments.
%C One half of the odd part of the bisection of A099924 is found in A203574.
%H É. Czabarka, R. Flórez, L. Junes, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Florez/florez12.html">A Discrete Convolution on the Generalized Hosoya Triangle</a>, Journal of Integer Sequences, 18 (2015), #15.1.6.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6, -11, 6, -1).
%F a(n) = A099924(2*n), n>=0.
%F O.g.f.: (4-11*x+11*x^2+x^3)/(1-3*x+x^2)^2.
%F a(n) = 4*(n+1)*F(2*n+1)-(2*n+1)*F(2*n), n>=0, with the Fibonacci numbers F(n)=A000045(n). From the partial fraction decomposition of the o.g.f. and the Fibonacci recurrence.
%F a(0)=4, a(1)=13, a(2)=45, a(3)=152, a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3)-a(n-4). - _Harvey P. Dale_, Jan 11 2014
%t CoefficientList[Series[(4-11x+11x^2+x^3)/(1-3x+x^2)^2,{x,0,30}],x] (* or *) LinearRecurrence[{6,-11,6,-1},{4,13,45,152},30] (* _Harvey P. Dale_, Jan 11 2014 *)
%Y Cf. A000032, A000045, A099924, 2*A203574.
%K nonn,easy
%O 0,1
%A _Wolfdieter Lang_, Jan 03 2012
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