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%I #18 Apr 11 2024 17:54:05
%S 1,2,4,5,10,14,25,38,64,101,166,266,433,698,1132,1829,2962,4790,7753,
%T 12542,20296,32837,53134,85970,139105,225074,364180,589253,953434,
%U 1542686,2496121,4038806,6534928,10573733,17108662,27682394,44791057,72473450,117264508
%N a(n) = 3*Fibonacci(n) + (-1)^n.
%C Binomial transform is A097134.
%H Reinhard Zumkeller, <a href="/A097133/b097133.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1).
%F G.f.: (1+2*x+2*x^2)/((1+x)*(1-x-x^2));
%F a(n) = 2*a(n-2)+a(n-3);
%F a(2*n) = 3*F(2*n)+1 = A097136(n).
%t CoefficientList[Series[(1+2x+2x^2)/((1+x)(1-x-x^2)),{x,0,40}],x] (* or *) LinearRecurrence[{0,2,1},{1,2,4},40] (* _Harvey P. Dale_, May 07 2011 *)
%o (Haskell)
%o a097133 n = a097133_list !! n
%o a097133_list = 1 : 2 : 4 : zipWith (+)
%o (map (* 2) $ tail a097133_list) a097133_list
%o -- _Reinhard Zumkeller_, Feb 24 2015
%Y Cf. A000045, A097134, A097136.
%K easy,nonn,changed
%O 0,2
%A _Paul Barry_, Jul 26 2004
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