A343543 a(n) = n*Lucas(2*n).

0, 3, 14, 54, 188, 615, 1932, 5901, 17656, 52002, 151270, 435633, 1244184, 3528759, 9949058, 27907470, 77933552, 216784731, 600935076, 1660672257, 4576522540, 12580566138, 34504747354, 94440719589, 257998970928, 703593828075, 1915713858422, 5208304147686

Offset: 0

Author

Harry Richman, Apr 19 2021

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1).

Crossrefs

Cf. A000032, A005248 (L(2n)), A146005 (n*L(n)), A317408 (n*Fib(2n)).

Programs

Magma

[n*Lucas(2*n) : n in [0..40]]; // Wesley Ivan Hurt, Apr 19 2021

Mathematica

Table[n*LucasL[2*n], {n, 0, 30}] (* Amiram Eldar, Apr 19 2021 *)

PARI

a(n) = n*(fibonacci(2*n+1)+fibonacci(2*n-1)) \\ Andrew Howroyd, Jan 01 2024

Formula

a(n) = n*A005248(n).

G.f.: x*(3 - 4*x + 3*x^2)/(1 - 3*x + x^2)^2.

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4). - Wesley Ivan Hurt, Apr 19 2021