%I #8 Jun 13 2015 00:51:33
%S 1,1,2,3,6,10,17,27,44,71,116,188,305,493,798,1291,2090,3382,5473,
%T 8855,14328,23183,37512,60696,98209,158905,257114,416019,673134,
%U 1089154,1762289,2851443,4613732,7465175,12078908,19544084,31622993,51167077
%N A transform of (1-x)/(1-2x).
%C A transform of A011782 under the mapping g(x)->(1/(1+x^3))g(x/(1+x^3))
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,2,0,-1).
%F G.f.: (1-x+x^3)/((1+x^3)*(1-2*x+x^3)).
%F a(n) = 2*a(n-1)-2*a(n-3)+2*a(n-4)-a(n-6).
%F a(n) = sum{k=0..floor(n/3), binomial(n-2*k, k)*(-1)^k*(2^(n-3*k)+0^(n-3*k))/2}.
%F a(n) = A057079(n+1)/6 +A000045(n+3)/2 -A010694(n)/6. - _R. J. Mathar_, Sep 21 2012
%Y Cf. A099505, A099508, A099516, A000071.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Oct 20 2004