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%I #12 Mar 10 2019 01:43:12
%S 1,2,3,6,11,21,40,76,145,276,526,1002,1909,3637,6929,13201,25150,
%T 47915,91286,173915,331337,631252,1202640,2291229,4365172,8316378,
%U 15844082,30185609,57508601,109563441,208736561,397677834,757642355,1443434582
%N Row sums of a triangle related to the Fibonacci polynomials.
%C Row sums of A109221.
%C The Kn4 sums, see A180662, of triangle A065941 equal the terms of this sequence a(n) while the Kn4 sums of triangle A194005 equal a(n+1)-1. - _Johannes W. Meijer_, Aug 14 2011
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,0,-1).
%F G.f.: (1 + x - x^2 - x^3)/(1 - x - 2x^2 + x^4);
%F a(n) = a(n-1) + 2a(n-2) - a(n-4);
%F a(n) = Sum_{k=0..n} binomial(floor((2n-k)/2)+n-k, 2n-2k).
%p A109222 := proc(n): add(binomial(floor((2*n-k)/2)+n-k, 2*n-2*k), k=0..n) end: seq(A109222(n), n=0..33); # _Johannes W. Meijer_, Aug 14 2011
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jun 22 2005