A099430 a(n) = 2^n+(-1)^n-1.

1, 0, 4, 6, 16, 30, 64, 126, 256, 510, 1024, 2046, 4096, 8190, 16384, 32766, 65536, 131070, 262144, 524286, 1048576, 2097150, 4194304, 8388606, 16777216, 33554430, 67108864, 134217726, 268435456, 536870910, 1073741824, 2147483646

Offset: 0

Author

Paul Barry, Oct 15 2004

Keywords

• easy
• nonn

Comments

Jacobsthal-Lucas numbers less 1.

For n >= 1, a(n) is also the number of periodic points of period n of the Period Doubling and the Thue-Morse Chain. [Natascha Neumaerker (naneumae(AT)math.uni-bielefeld.de), Apr 06 2009]

Links

• N. Neumarker, Realizability of Integer Sequences as Differences of Fixed Point Count Sequences, JIS 12 (2009) 09.4.5, Example 9.
• Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Crossrefs

Cf. A014551.

Programs

Mathematica

LinearRecurrence[{2,1,-2},{1,0,4},40] (* Harvey P. Dale, Nov 07 2017 *)

PARI

a(n)=2^n+(-1)^n-1 \\ Charles R Greathouse IV, May 09 2016

Formula

G.f.: (1-2x+3x^2)/((1-x)(1-x-2x^2)) = (1-2x+3x^2)/((1-x^2)(1-2x)).

a(n) = A014551(n)-1.

zeta(z) = (1-z)/((1+z)(1-2z)). [Natascha Neumaerker (naneumae(AT)math.uni-bielefeld.de), Apr 06 2009]

a(n) = 2*a(n-1)+a(n-2)-2*a(n-3). - Wesley Ivan Hurt, Jun 09 2023