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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2, 1, -2).

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)

a(n) ~ 4*2^n. - Charles R Greathouse IV, May 31 2026

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 *)

Prog

(Magma) [2^(n+2)-3-(-1)^n: n in [0..30]]; // Vincenzo Librandi, Apr 03 2012
(PARI) a(n)=4*2^n-3-(-1)^n \\ Charles R Greathouse IV, May 31 2026

Crossrefs

Cf. A000975, A026644, A020988.

Sequence in context: A357197 A322374 A351694 * A236539 A122211 A015801

Adjacent sequences: A014128 A014129 A014130 * A014132 A014133 A014134

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved