A269019 a(n) = 2^n + 2*(-1)^n - 1.

2, -1, 5, 5, 17, 29, 65, 125, 257, 509, 1025, 2045, 4097, 8189, 16385, 32765, 65537, 131069, 262145, 524285, 1048577, 2097149, 4194305, 8388605, 16777217, 33554429, 67108865, 134217725, 268435457, 536870909, 1073741825, 2147483645, 4294967297, 8589934589

Offset

0,1

Comments

Fermat numbers > 3 from A000215 are terms.

Prime terms are in A269018.

Union of A052539 and A267921.

Links

Table of n, a(n) for n=0..33.

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

Formula

G.f.: (2-5*x+5*x^2)/((1-2*x)*(1-x^2)). - Vincenzo Librandi, Feb 18 2016

Example

For n = 6; a(n) = 2^n + 2*(-1)^n - 1 = 2^6 + 2*(-1)^6 - 1 = 65.

Mathematica

Table [2^n + 2 (-1)^n - 1, {n, 0, 80}] (* or *) CoefficientList[Series[(2 - 5 x + 5 x^2) / ((1 - 2 x) (1 - x^2)), {x, 0, 33}], x] (* Vincenzo Librandi, Feb 18 2016 *)
LinearRecurrence[{2, 1, -2}, {2, -1, 5}, 40] (* Harvey P. Dale, Feb 25 2022 *)

Prog

(Magma) [2^n + 2*(-1)^n - 1: n in [0..300]];

Crossrefs

Cf. A019434, A052539, A092506, A176680, A267921, A269018.

Sequence in context: A167638 A317878 A209108 * A184234 A193816 A335136

Adjacent sequences: A269016 A269017 A269018 * A269020 A269021 A269022

Keyword

sign

Author

Jaroslav Krizek, Feb 17 2016

Status

approved