A156589 a(n) = 4^n - 2^n - 1.

-1, 1, 11, 55, 239, 991, 4031, 16255, 65279, 261631, 1047551, 4192255, 16773119, 67100671, 268419071, 1073709055, 4294901759, 17179738111, 68719214591, 274877382655, 1099510579199, 4398044413951, 17592181850111, 70368735789055

Offset: 0

Author

M. F. Hasler, Feb 10 2009

Keywords

• sign
• easy

Comments

Sequence A098845 lists indices of primes, i.e., a(n) prime <=> n=A098845(k) for some k.

Starting with n=2, binary numbers of the form (n-1)0(n) where n is the index and the number of 1's. It can also be formed by appending a 1 to the right of each term of A129868.

1/a(n) = Sum_{m>0} A000045(m)*2^(-n(m+1)) for n > 0. E.g., 1/a(4) = 0.0000 0001 0001 0010 0011 0101 1000 ... in binary. - Lee A. Newberg, Apr 12 2018

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A000045, A098845, A129868.

Programs

Magma

[4^n-2^n-1: n in [0..30]]; // Vincenzo Librandi, Apr 13 2018

Mathematica

Table[4^n - 2^n - 1, {n, 0, 25}] (* Vincenzo Librandi, Apr 13 2018 *)

PARI

vector(99,n,4^n-2^n-1)

Formula

G.f.: ( 1-8*x+10*x^2 ) / ( (-1+x)*(2*x-1)*(4*x-1) ). - R. J. Mathar, Oct 21 2014