A146005 a(n) = n*Lucas(n).

0, 1, 6, 12, 28, 55, 108, 203, 376, 684, 1230, 2189, 3864, 6773, 11802, 20460, 35312, 60707, 104004, 177631, 302540, 513996, 871266, 1473817, 2488368, 4194025, 7057518, 11858508, 19898116, 33345679, 55814940, 93320819, 155867104

Offset: 0

Author

R. J. Mathar, Oct 26 2008

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1).

Programs

Magma

I:=[0, 1, 6, 12]; [n le 4 select I[n] else 2*Self(n-1) + Self(n-2) - 2*Self(n-3) - Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 13 2012

Mathematica

Table[LucasL[n, 1]*n, {n, 0, 36}] (* Zerinvary Lajos, Jul 09 2009 *)
CoefficientList[Series[x * (1 + 4*x - x^2)/(1 - x - x^2)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 13 2012 *)
LinearRecurrence[{2,1,-2,-1},{0,1,6,12},40] (* Harvey P. Dale, Apr 03 2013 *)

Formula

a(n) = n*A000032(n).

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

a(n) = 2*a(n-1)+a(n-2)-2*a(n-3)-a(n-4).

a(n) = A000045(n)-5*A000045(n+1)+5*A010049(n+1).

a(n) = A045925(n)+2*A099920(n-1).

E.g.f.: x*exp(x/2)*(cosh(sqrt(5)*x/2) + sqrt(5)*sinh(sqrt(5)*x/2)). - G. C. Greubel, Jan 30 2016