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%I #16 Sep 08 2022 08:46:12
%S 0,2,7,14,31,60,116,216,397,718,1285,2278,4008,7006,12179,21070,36299,
%T 62304,106588,181812,309305,524942,888977,1502474,2534736,4269050,
%U 7178911,12054926,20215927,33859908,56646980,94667088,158045413,263604046,439272349
%N a(n) = Fibonacci(n) + n*Lucas(n).
%H Bruno Berselli, <a href="/A258321/b258321.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2,-1).
%F G.f.: x*(2 + 3*x - 2*x^2)/(1 - x - x^2)^2.
%F a(n) = -a(-n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4).
%F a(n) = (n+1)*Fibonacci(n+1) + (n-1)*Fibonacci(n-1).
%F a(n) = 2*A001629(n+1) + 3*A001629(n) - 2*A001629(n-1) for n>0.
%F Sum_{i>0} 1/a(i) = .782177794921758720...
%t Table[Fibonacci[n] + n LucasL[n], {n, 0, 40}] (* or *) LinearRecurrence[{2, 1, -2, -1}, {0, 2, 7, 14}, 40]
%o (Sage) [fibonacci(n)+n*lucas_number2(n, 1, -1) for n in (0..40)]
%o (Magma) [Fibonacci(n)+n*Lucas(n): n in [0..40]]
%Y Cf. A061705: n*Fibonacci(n)+Lucas(n) = (n+1)*Fibonacci(n+1)-(n-1)*Fibonacci(n-1) with n>0.
%Y Cf. A000032, A000045, A001629.
%K nonn,easy
%O 0,2
%A _Bruno Berselli_, May 26 2015
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