A133673 a(n) = n*L(n) + (n-1)*L(n-1) where L(n) is the Lucas number.

7, 18, 40, 83, 163, 311, 579, 1060, 1914, 3419, 6053, 10637, 18575, 32262, 55772, 96019, 164711, 281635, 480171, 816536, 1385262, 2345083, 3962185, 6682393, 11251543, 18916026, 31756624, 53243795, 89160619, 149135759, 249187923, 415946572, 693648930

Offset: 2

Author

Parthasarathy Nambi, Dec 29 2007

Keywords

• nonn
• easy

Comments

For n>2, two evens followed by four odds.

Examples

			For n=2, a(2) = 7;
For n=21, a(21) = 816536.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1).

Crossrefs

Cf. A000032, A136376, A146005.

Programs

Mathematica

Total/@Partition[Times@@@Table[{n,LucasL[n]},{n,30}],2,1] (* or *) LinearRecurrence[{2,1,-2,-1},{7,18,40,83},30](* Harvey P. Dale, Oct 21 2011 *)

Formula

From R. J. Mathar, Jul 08 2009, Jul 13 2009: (Start)

G.f.: -x^2*(-7-4*x+3*x^2+x^3)/(x^2+x-1)^2.

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

a(n) = A146005(n) + A146005(n-1). (End)

Extensions

Typo in A-numbers corrected by R. J. Mathar, Jul 13 2009

More terms from Harvey P. Dale, Oct 21 2011