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%I #64 Aug 16 2024 19:18:23
%S 9,18,36,72,144,288,576,1152,2304,4608,9216,18432,36864,73728,147456,
%T 294912,589824,1179648,2359296,4718592,9437184,18874368,37748736,
%U 75497472,150994944,301989888,603979776,1207959552,2415919104,4831838208,9663676416,19327352832
%N a(n) = 9*2^n.
%C Row sums of (8, 1)-Pascal triangle A093565. - _N. J. A. Sloane_, Sep 22 2004
%C The first differences are the sequence itself. - _Alexandre Wajnberg_ & _Eric Angelini_, Sep 07 2005
%C 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
%C 9 times powers of 2. - _Omar E. Pol_, Dec 16 2008
%C a(n) = A173786(n+3,n) for n>2. - _Reinhard Zumkeller_, Feb 28 2010
%C 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
%H Vincenzo Librandi, <a href="/A005010/b005010.txt">Table of n, a(n) for n = 0..235</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).
%F a(n) = 9*2^n.
%F G.f.: 9/(1-2*x).
%F a(n) = A118416(n+1,5) for n>4. - _Reinhard Zumkeller_, Apr 27 2006
%F a(n) = 2*a(n-1), n>0; a(0)=9. - _Philippe Deléham_, Nov 23 2008
%F a(n) = 9*A000079(n). - _Omar E. Pol_, Dec 16 2008
%F a(n) = 3*A007283(n). - _Omar E. Pol_, Jul 14 2015
%F E.g.f.: 9*exp(2*x). - _Elmo R. Oliveira_, Aug 16 2024
%t 9*2^Range[0, 60] (* _Vladimir Joseph Stephan Orlovsky_, Jun 09 2011 *)
%o (Magma) [9*2^n: n in [0..40]]; // _Vincenzo Librandi_, Apr 28 2011
%o (PARI) a(n)=9<<n \\ _Charles R Greathouse IV_, Apr 17 2012
%Y Cf. A000079, A093565, A173786, A118416, A007283.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Jun 14 1998