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%I #6 Aug 09 2016 15:45:05
%S 1,2,4,12,20,64,104,336,544,1760,2848,9216,14912,48256,78080,252672,
%T 408832,1323008,2140672,6927360,11208704,36272128,58689536,189923328,
%U 307302400,994451456,1609056256,5207015424,8425127936,27264286720
%N Row sums of triangle A099602, in which row n equals the inverse binomial transform of column n of the triangle of trinomial coefficients (A027907).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,6,0,-4).
%F a(n) = fibonacci(n+1)*2^[(n+1)/2]. a(n) = 6*a(n-2) - 4*a(n-4) for n>4. G.f.: (1+2*x-2*x^2)/(1-6*x^2+4*x^4).
%e Sequence begins: {1*1, 1*2, 2*2, 3*4, 5*4, 8*8, 13*8, 21*16, 34*16, ...}.
%t LinearRecurrence[{0,6,0,-4},{1,2,4,12},30] (* _Harvey P. Dale_, Aug 09 2016 *)
%o (PARI) a(n)=fibonacci(n+1)*2^((n+1)\2)
%Y Cf. A000045, A099602.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 25 2004