|
%I #18 Jan 01 2024 19:50:06
%S 0,3,14,54,188,615,1932,5901,17656,52002,151270,435633,1244184,
%T 3528759,9949058,27907470,77933552,216784731,600935076,1660672257,
%U 4576522540,12580566138,34504747354,94440719589,257998970928,703593828075,1915713858422,5208304147686
%N a(n) = n*Lucas(2*n).
%H Andrew Howroyd, <a href="/A343543/b343543.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 (6,-11,6,-1).
%F G.f.: x*(3 - 4*x + 3*x^2)/(1 - 3*x + x^2)^2.
%F a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4). - _Wesley Ivan Hurt_, Apr 19 2021
%t Table[n*LucasL[2*n], {n, 0, 30}] (* _Amiram Eldar_, Apr 19 2021 *)
%o (Magma) [n*Lucas(2*n) : n in [0..40]]; // _Wesley Ivan Hurt_, Apr 19 2021
%o (PARI) a(n) = n*(fibonacci(2*n+1)+fibonacci(2*n-1)) \\ _Andrew Howroyd_, Jan 01 2024
%Y Cf. A000032, A005248 (L(2n)), A146005 (n*L(n)), A317408 (n*Fib(2n)).
%K nonn,easy
%O 0,2
%A _Harry Richman_, Apr 19 2021
|
