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%I #10 Mar 10 2023 10:49:34
%S 1,4,15,49,154,473,1437,4340,13067,39277,117954,354061,1062505,
%T 3188036,9564951,28696217,86090858,258276145,774834213,2324511988,
%U 6973551091,20920677749,62762072850,188286282629,564858951569,1694577022468
%N G.f.: (1+x^2)/((1-3x)(1-x-x^2)).
%C A Lucas convolution.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-3).
%F a(n)=4a(n-1)-2a(n-2)-3a(n-3); a(n)=2*3^n-Fib(n+2); a(n)=sum{k=0..n, (L(k)-0^k)3^(n-k)}.
%F a(n) = A094688(n-1)+A094688(n+1). - _R. J. Mathar_, Sep 27 2014
%t CoefficientList[Series[(1+x^2)/((1-3x)(1-x-x^2)),{x,0,40}],x] (* or *) LinearRecurrence[ {4,-2,-3},{1,4,15},40] (* _Harvey P. Dale_, Mar 10 2023 *)
%Y Cf. A000032, A000045.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Oct 01 2004
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