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A256233 a(n) = L(2*n+1) - 2, where L is A000032.

%I A256233 #30 Sep 08 2022 08:46:11
%S A256233 -1,2,9,27,74,197,519,1362,3569,9347,24474,64077,167759,439202,
%T A256233 1149849,3010347,7881194,20633237,54018519,141422322,370248449,
%U A256233 969323027,2537720634,6643838877,17393795999,45537549122,119218851369,312119004987,817138163594
%N A256233 a(n) = L(2*n+1) - 2, where L is A000032.
%H A256233 Colin Barker, <a href="/A256233/b256233.txt">Table of n, a(n) for n = 0..1000</a>
%H A256233 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,1).
%F A256233 G.f.: (-1+6*x-3*x^2)/((1-x)*(1-3*x+x^2)).
%F A256233 a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3).
%F A256233 a(n) = (-2+(2^(-1-n)*((3-sqrt(5))^n*(-5+sqrt(5))+(3+sqrt(5))^n*(5+sqrt(5))))/sqrt(5)). - _Colin Barker_, Nov 03 2016
%t A256233 Table[LucasL[n] - 2, {n, 1, 70, 2}] (* or *) LinearRecurrence[{4, -4, 1}, {-1, 2, 9}, 40]
%o A256233 (Magma) [Lucas(n)-2: n in [1..70 by 2]];
%o A256233 (PARI) Vec((-1+6*x-3*x^2)/((1-x)*(1-3*x+x^2)) + O(x^40)) \\ _Colin Barker_, Nov 03 2016
%o A256233 (PARI) L(n) = round(((1+sqrt(5))/2)^n + ((1-sqrt(5))/2)^n)
%o A256233 vector(30, n, n--; L(2*n+1)-2) \\ _Colin Barker_, Nov 03 2016
%Y A256233 Cf. A000032, A004146.
%K A256233 sign,easy
%O A256233 0,2
%A A256233 _Vincenzo Librandi_, Mar 20 2015
%E A256233 Incorrect comment about A004146 removed by _Georg Fischer_, Sep 04 2020