A014131 a(n) = 2*a(n-1) if n odd else 2*a(n-1) + 6.

0, 6, 12, 30, 60, 126, 252, 510, 1020, 2046, 4092, 8190, 16380, 32766, 65532, 131070, 262140, 524286, 1048572, 2097150, 4194300, 8388606, 16777212, 33554430, 67108860, 134217726, 268435452, 536870910

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2, 1, -2).

Crossrefs

Cf. A000975.

Programs

Magma

[2^(n+2)-3-(-1)^n: n in [0..30]]; // Vincenzo Librandi, Apr 03 2012

Mathematica

Table[2^(n+2)-3-(-1)^n,{n,0,40}] (* or *) CoefficientList[Series[6x/((1-2x)(1-x)(1+x)),{x,0,30}],x] (* Vincenzo Librandi, Apr 03 2012 *)
nxt[{n_,a_}]:={n+1,If[EvenQ[n],2a,2a+6]}; NestList[nxt,{1,0},30][[;;,2]] (* or *) LinearRecurrence[ {2,1,-2},{0,6,12},30] (* Harvey P. Dale, Aug 26 2024 *)

Formula

a(n) = 3*A026644(n), n > 0. [moved from A020988 by R. J. Mathar, Oct 21 2008]

From R. J. Mathar, Oct 21 2008: (Start)

G.f.: 6x/((1-2x)(1-x)(1+x)).

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