A166542 a(n) = 6*n - a(n-1), with n>1, a(1)=2.

2, 10, 8, 16, 14, 22, 20, 28, 26, 34, 32, 40, 38, 46, 44, 52, 50, 58, 56, 64, 62, 70, 68, 76, 74, 82, 80, 88, 86, 94, 92, 100, 98, 106, 104, 112, 110, 118, 116, 124, 122, 130, 128, 136, 134, 142, 140, 148, 146, 154, 152, 160, 158, 166, 164, 172, 170, 178, 176, 184

Offset: 1

Author

Vincenzo Librandi, Oct 16 2009

Keywords

• nonn
• easy

Links

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

Programs

Magma

[n eq 1 select 2 else 6*n-Self(n-1): n in [1..80]]; // Vincenzo Librandi, Sep 13 2013

Mathematica

CoefficientList[Series[-(- 2 - 8 x + 4 x^2)/((1 + x) (x - 1)^2), {x, 0, 80}], x] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{1,1,-1}, {2, 10, 8}, 50] (* G. C. Greubel, May 16 2016 *)

Formula

G.f.: -x*(-2-8*x+4*x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 13 2013

From G. C. Greubel, May 16 2016: (Start)

E.g.f.: (1/2)*(3*(1 + 2*x)*exp(x) + 5*exp(-x) - 8).

a(n) = a(n-1) + a(n-2) - a(n-3). (End)

a(n) = 2*A166517(n). - Philippe Deléham, Nov 29 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = 1/4 + Pi/(6*sqrt(3)). - Amiram Eldar, Feb 23 2023