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%I #15 Jan 22 2020 15:06:22
%S 1,2,4,8,17,38,87,200,458,1044,2373,5388,12233,27782,63112,143392,
%T 325805,740266,1681935,3821412,8682310,19726316,44818473,101828344,
%U 231355953,525645354,1194276812,2713420728,6164945513,14006877390
%N Row sums of a Pascal-Fibonacci triangle.
%C Binomial transform of double Fibonacci sequence A103609(n+2). Row sums of A114197.
%H Michael De Vlieger, <a href="/A114199/b114199.txt">Table of n, a(n) for n = 0..2806</a>
%H Sergio Falcón, <a href="https://www.rgnpublications.com/journals/index.php/cma/article/viewFile/1221/950">Binomial Transform of the Generalized k-Fibonacci Numbers</a>, Communications in Mathematics and Applications (2019) Vol. 10, No. 3, 643-651.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2,1)
%F G.f.: (1-x)^2/(1-4x+5x^2-2x^3-x^4);
%F a(n) = Sum_{k=0..n} Sum_{j=0..n-k} C(n-k, j)*C(k, j)*F(j);
%F a(n) = Sum_{k=0..n} C(n, k)*F(floor((k+2)/2)).
%t LinearRecurrence[{4,-5,2,1},{1,2,4,8},30] (* _Harvey P. Dale_, Dec 07 2015 *)
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 16 2005
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