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%I #9 Oct 26 2022 03:06:34
%S 1,1,3,7,19,56,138,407,999,2851,7113,19702,49954,135461,347553,929567,
%T 2403759,6374236,16564458,43697227,113896339,299525051,782121453,
%U 2053027082,5366641794,14071792681,36807232413,96449857207,252375716899,661078086176,1730190463338,4531099045727
%N a(n) = A142710(n)/2.
%H G. C. Greubel, <a href="/A147586/b147586.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,7,-12,-11,16,-4).
%F From _G. C. Greubel_, Oct 26 2022: (Start)
%F a(n) = (1/2)*( (-1)^n*LucasL(n) + LucasL(2*n) - (1 + (-1)^n)*2^(n-1) - [n=0]).
%F a(n) = 2*a(n-1) + 7*a(n-2) - 12*a(n-3) - 11*a(n-4) + 16*a(n-5) - 4*a(n-6), n >= 7.
%F G.f.: (1 - x - 6*x^2 + 6*x^3 + 7*x^4 - 2*x^6)/((1 - 4*x^2)*(1 + x - x^2)*(1 - 3*x + x^2)). (End)
%t LinearRecurrence[{2,7,-12,-11,16,-4}, {1,1,3,7,19,56,138}, 51] (* _G. C. Greubel_, Oct 26 2022 *)
%o (Magma) [n eq 0 select 1 else ((-1)^n*Lucas(n) +Lucas(2*n) -(1+(-1)^n)*2^(n-1))/2: n in [0..50]]; // _G. C. Greubel_, Oct 26 2022
%o (SageMath)
%o def A147586(n): return ((-1)^n*lucas_number2(n,1,-1) + lucas_number2(2*n,1,-1) - (1 + (-1)^n)*2^(n-1) -int(n==0))/2
%o [A147586(n) for n in range(51)] # _G. C. Greubel_, Oct 26 2022
%Y Cf. A000032, A142710.
%K nonn
%O 0,3
%A _Paul Curtz_, Nov 08 2008
%E Terms a(11) onward added by _G. C. Greubel_, Oct 26 2022
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