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Sum of Lucas numbers and inverted Lucas numbers: a(n) = A000032(n)*A075193(n).
1

%I #9 Jul 14 2022 22:43:50

%S 3,-2,7,-3,18,-7,47,-18,123,-47,322,-123,843,-322,2207,-843,5778,

%T -2207,15127,-5778,39603,-15127,103682,-39603,271443,-103682,710647,

%U -271443,1860498,-710647,4870847,-1860498,12752043,-4870847,33385282,-12752043,87403803,-33385282,228826127,-87403803

%N Sum of Lucas numbers and inverted Lucas numbers: a(n) = A000032(n)*A075193(n).

%C a(n) = (1 + (-1)^n)*L(n) + ((-1)^n)*L(n-1), L(n) Lucas numbers.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-1).

%F a(n) = 3*a(n-2) - a(n-4); a(0)=3, a(1)=-2, a(2)=7, a(3)=-3.

%F O.g.f. (3-2*x-2*x^2+3*x^3)/(1-3*x^2+x^4).

%t CoefficientList[Series[(3-2x-2x^2+3x^3)/(1-3x^2+x^4), {x, 0, 40}], x]

%Y Cf. A000032, A075193.

%K easy,sign

%O 0,1

%A Mario Catalani (mario.catalani(AT)unito.it), Sep 12 2002