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

2,1

Comments

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

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).

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)

Example

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

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 *)

Crossrefs

Cf. A000032, A136376, A146005.

Sequence in context: A263876 A192751 A272459 * A023166 A002764 A124053

Adjacent sequences: A133670 A133671 A133672 * A133674 A133675 A133676

Keyword

nonn,easy

Author

Parthasarathy Nambi, Dec 29 2007

Extensions

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

More terms from Harvey P. Dale, Oct 21 2011

Status

approved