A168379 a(n) = 4*n - 2*(-1)^n + 1.

7, 7, 15, 15, 23, 23, 31, 31, 39, 39, 47, 47, 55, 55, 63, 63, 71, 71, 79, 79, 87, 87, 95, 95, 103, 103, 111, 111, 119, 119, 127, 127, 135, 135, 143, 143, 151, 151, 159, 159, 167, 167, 175, 175, 183, 183, 191, 191, 199, 199, 207, 207, 215, 215, 223, 223, 231, 231

Offset: 1

Author

Vincenzo Librandi, Nov 24 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

[4*n -2*(-1)^n + 1: n in [1..70]]; // Vincenzo Librandi, Sep 18 2013

Maple

A168379:=n->4*n - 2*(-1)^n + 1: seq(A168379(n), n=1..100); # Wesley Ivan Hurt, Apr 26 2017

Mathematica

Table[4 n - 2 (-1)^n + 1, {n, 60}] (* Bruno Berselli, Sep 18 2013 *)
CoefficientList[Series[(7 + x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 18 2013 *)

Formula

a(n) = 8*n - a(n-1) - 2, with n>1, a(1)=7.

G.f.: x*(7 + x^2)/((1+x)*(1-x)^2). - Vincenzo Librandi, Sep 18 2013

a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 18 2013

a(n) = 7 + 8*floor((n-1)/2). - Bruno Berselli, Sep 18 2013

E.g.f.: (-2 + exp(x) + (4*x + 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 19 2016

Extensions

Definition rewritten by Vincenzo Librandi, Sep 18 2013