A168326 a(n) = (6*n - 3*(-1)^n - 1)/2.

4, 4, 10, 10, 16, 16, 22, 22, 28, 28, 34, 34, 40, 40, 46, 46, 52, 52, 58, 58, 64, 64, 70, 70, 76, 76, 82, 82, 88, 88, 94, 94, 100, 100, 106, 106, 112, 112, 118, 118, 124, 124, 130, 130, 136, 136, 142, 142, 148, 148, 154, 154, 160, 160, 166, 166, 172, 172, 178, 178

Offset: 1

Author

Vincenzo Librandi, Nov 23 2009

Keywords

• nonn
• easy
• less

Links

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

Crossrefs

Cf. A016957, A168236.

Programs

Magma

[n eq 1 select n+3 else 6*n-Self(n-1)-4: n in [1..70]]; // Vincenzo Librandi, Sep 17 2013

Mathematica

With[{c = 6 Range[0, 30] + 4}, Riffle[c, c]] (* or *) RecurrenceTable[ {a[1] == 4, a[n] == 6 n - a[n-1] - 4}, a, {n, 60}] (* Harvey P. Dale, Jun 12 2012 *)
Table[3 n - 3 (-1)^n/2 - 1/2, {n, 70}] (* Bruno Berselli, Sep 17 2013 *)
CoefficientList[Series[(4 + 2 x^2) / ((1 + x) (1 - x)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 17 2013 *)

Formula

a(n) = 6*n - a(n-1) - 4, with n>1, a(1)=4.

From Vincenzo Librandi, Sep 17 2013: (Start)

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

a(n) = 2*A168236(n) = A168300(n) - 1 = A168329(n) + 1 = A168301(n+1) - 3.

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

E.g.f.: (1/2)*(-3 + 4*exp(x) + (6*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 18 2016

Extensions

New definition by Bruno Berselli, Sep 17 2013