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
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).
Programs
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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).
Extensions
Typo in A-numbers corrected by R. J. Mathar, Jul 13 2009
More terms from Harvey P. Dale, Oct 21 2011
Comments