A005010 a(n) = 9*2^n.

9, 18, 36, 72, 144, 288, 576, 1152, 2304, 4608, 9216, 18432, 36864, 73728, 147456, 294912, 589824, 1179648, 2359296, 4718592, 9437184, 18874368, 37748736, 75497472, 150994944, 301989888, 603979776, 1207959552, 2415919104, 4831838208, 9663676416, 19327352832

Offset: 0

Author

N. J. A. Sloane, Jun 14 1998

Keywords

• nonn
• easy

Comments

Row sums of (8, 1)-Pascal triangle A093565. - N. J. A. Sloane, Sep 22 2004

The first differences are the sequence itself. - Alexandre Wajnberg & Eric Angelini, Sep 07 2005

For n>=1, a(n) is equal to the number of functions f:{1,2,...,n+2}->{1,2,3} such that for fixed, different x_1, x_2,...,x_n in {1,2,...,n+2} and fixed y_1, y_2,...,y_n in {1,2,3} we have f(x_i)<>y_i, (i=1,2,...,n). - Milan Janjic, May 10 2007

9 times powers of 2. - Omar E. Pol, Dec 16 2008

a(n) = A173786(n+3,n) for n>2. - Reinhard Zumkeller, Feb 28 2010

Let D(m) = {d(m,i)}, i = 1..q, denote the set of the q divisors of a number m, and consider s0(m) and s1(m) the sums of the divisors that are congruent to 2 and 3 (mod 4) respectively. For n>0, the sequence a(n) lists the numbers m such that s0(m) = 26 and s1(m) = 3. - Michel Lagneau, Feb 10 2017

Links

• Mia Boudreau, Table of n, a(n) for n = 0..3000 (first 236 terms from Vincenzo Librandi)
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (2).

Crossrefs

Cf. A000079, A093565, A173786, A118416, A007283.

Programs

Magma

[9*2^n: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011

Mathematica

9*2^Range[0, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)

PARI

a(n)=9<Charles R Greathouse IV, Apr 17 2012

Formula

a(n) = 9*2^n.

G.f.: 9/(1-2*x).

a(n) = A118416(n+1,5) for n>4. - Reinhard Zumkeller, Apr 27 2006

a(n) = 2*a(n-1), n>0; a(0)=9. - Philippe Deléham, Nov 23 2008

a(n) = 9*A000079(n). - Omar E. Pol, Dec 16 2008

a(n) = 3*A007283(n). - Omar E. Pol, Jul 14 2015

E.g.f.: 9*exp(2*x). - Elmo R. Oliveira, Aug 16 2024