A153234 a(n) = floor(2^n/9).

0, 0, 0, 0, 1, 3, 7, 14, 28, 56, 113, 227, 455, 910, 1820, 3640, 7281, 14563, 29127, 58254, 116508, 233016, 466033, 932067, 1864135, 3728270, 7456540, 14913080, 29826161, 59652323, 119304647, 238609294, 477218588, 954437176, 1908874353, 3817748707, 7635497415, 15270994830

Offset: 0

Author

Paul Curtz, Dec 21 2008

Keywords

• nonn
• easy

Comments

Partial sums of A113405. - Mircea Merca, Dec 28 2010

Dubickas proves that infinitely many terms of this sequence are composite. - Charles R Greathouse IV, Feb 04 2016

Parity from a(4) onward gives A088911 (Period 6: repeat [1, 1, 1, 0, 0, 0]). - Jeremy Gardiner, Nov 04 2020

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Artūras Dubickas, Prime and composite integers close to powers of a number, Monatsh. Math. 158:3 (2009), pp. 271-284.
• Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,3,-2).

Crossrefs

Cf. A113405.

Programs

Magma

[Round((2*2^n-9)/18): n in [0..40]]; // Vincenzo Librandi, Jun 25 2011

Maple

seq(floor(2^n/9),n=0..25); # Mircea Merca, Dec 28 2010

Mathematica

Table[Floor[2^n/9], {n, 0, 37}] (* Michael De Vlieger, Mar 26 2016 *)

PARI

a(n)=2^n\9 \\ Charles R Greathouse IV, Oct 07 2015

PARI

x='x+O('x^44); concat(vector(4), Vec(x^4/((x-1)*(2*x-1)*(1+x)*(x^2-x+1)))) \\ Altug Alkan, Mar 25 2016

Sage

[floor(2^n/9) for n in (0..40)] # G. C. Greubel, Jun 05 2019

Formula

a(n+1) - 2*a(n) = A088911(n+3).

a(n) + a(n+3) = 2^n - 1 = A000225(n), n > 0.

From Mircea Merca, Dec 28 2010: (Start)

a(n) = round((2*2^n-9)/18) = floor((2^n-1)/9) = ceiling((2^n-8)/9).

a(n) = a(n-6) + 7*2^(n-6), n > 5. (End)

a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + 3*a(n-4) - 2*a(n-5).

G.f.: x^4 / ( (1-2*x)*(1-x^2)*(1-x+x^2) ).

a(n) + a(n+1) = A111927(n). - R. J. Mathar, Apr 08 2013

Extensions

More terms from Vincenzo Librandi, Jun 25 2011