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%I #25 Jan 01 2024 19:46:58
%S 1,12,55,203,684,2189,6773,20460,60707,177631,513996,1473817,4194025,
%T 11858508,33345679,93320819,260079468,722163365,1998685277,5515470636,
%U 15180186491,41680890247,114197428620,312260427313,852296004049,2322415005324,6318599122663,17166545274395
%N a(n) = (2*n+1)*Lucas(2*n+1).
%H Andrew Howroyd, <a href="/A343539/b343539.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.: (1-x)*(1 + 7*x + x^2)/(1 - 3*x + x^2)^2.
%F a(n) = (2*n+1)*A000032(2*n+1).
%F a(n) = A146005(2*n+1).
%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[(2n+1) LucasL[2n+1], {n, 0, 30}] (* _Wesley Ivan Hurt_, Apr 19 2021 *)
%o (Magma) [(2*n+1)*Lucas(2*n+1) : n in [0..40]]; // _Wesley Ivan Hurt_, Apr 19 2021
%o (PARI) a(n) = (2*n+1)*(fibonacci(2*n+2)+fibonacci(2*n)) \\ _Andrew Howroyd_, Jan 01 2024
%Y Bisection of A146005.
%Y Cf. A000032, A002878.
%K nonn,easy
%O 0,2
%A _Harry Richman_, Apr 16 2021
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