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%I #29 Mar 28 2024 16:11:46
%S 1,2,6,19,60,188,589,1846,5786,18135,56840,178152,558377,1750106,
%T 5485310,17192459,53885860,168892996,529356757,1659148590,5200224626,
%U 16298923631,51085276240,160115201936,501844754065,1572918462066,4929955864374,15451827549123
%N Diagonal sums of triangle A185384.
%H Vincenzo Librandi, <a href="/A208481/b208481.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 (3,0,1,1).
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)*F(2*n-3*k+1), where F(n) are the Fibonacci numbers (A000045).
%F G.f.: (1 - x)/(1 - 3*x - x^3 - x^4).
%F a(n) = 3*a(n-1) + a(n-3) + a(n-4).
%t Table[Sum[Binomial[n-k,k]Fibonacci[2n-3k+1],{k,0,Floor[n/2]}],{n,0,100}]
%o (Maxima) makelist(sum(binomial(n-k,k)*fib(2*n-3*k+1),k,0,floor(n/2)),n,0,27);
%Y Cf. A185384.
%K nonn,easy
%O 0,2
%A _Emanuele Munarini_, Feb 29 2012
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