OFFSET
0,1
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).
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
MATHEMATICA
9*2^Range[0, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)
PROG
(Magma) [9*2^n: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011
(PARI) a(n)=9<<n \\ Charles R Greathouse IV, Apr 17 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 14 1998
STATUS
approved