Search: id:A038754
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%I A038754
%S A038754 1,2,3,6,9,18,27,54,81,162,243,486,729,1458,2187,4374,6561,13122,19683,
%T A038754 39366,59049,118098,177147,354294,531441,1062882,1594323,3188646,
%U A038754 4782969,9565938,14348907,28697814,43046721,86093442,129140163
%N A038754 a(2n)=3^n, a(2n+1)=2*3^n.
%C A038754 In general, for the recurrence a(n)=a(n-1)*a(n-2)/a(n-3), all terms are 
               integers iff a(0) divides a(2) and first three terms are positive 
               integers, since a(2n+k)=a(k)*(a(2)/a(0))^n for all nonnegative integers 
               n and k
%C A038754 a(n) = A140740(n+2,2). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 26 2008
%C A038754 See A133626 for an essentially identical sequence. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jun 08 2008
%H A038754 T. D. Noe, <a href="b038754.txt">Table of n, a(n) for n=0..400</a>
%H A038754 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A038754 a(n)=a(n-1)*a(n-2)/a(n-3) with a(0)=1, a(1)=2, a(2)=3.
%F A038754 a(2n)=(3/2)*a(2n-1)=3^n, a(2n+1)=2*a(2n)=2*3^n.
%F A038754 a(1)=1, a(n)=a(n-1)+1 if a(n-1) is odd, or a(n-1)=3/2*a(n-1) if a(n-1) 
               is even. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 27 2003
%F A038754 a(n)=(1/6)*(5-(-1)^n)*3^floor(n/2); a(2n)=a(2n-1)+a(2n-2)+a(2n-3); a(2n+1)=a(2n)+a(2n-1) 
               - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 27 2003
%F A038754 G.f.: (1+2x)/(1-3x^2) - Paul Barry (pbarry(AT)wit.ie), Aug 25 2003
%F A038754 a(n) = (1 + n mod 2) * 3^floor(n/2). a(n) = A087503(n) - A087503(n-1). 
               - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 11 2003
%F A038754 a(n)=sqrt(3)(2+sqrt(3))(sqrt(3))^n/6-sqrt(3)(2-sqrt(3))(-sqrt(3))^n/6 
               - Paul Barry (pbarry(AT)wit.ie), Sep 16 2003
%F A038754 a(n+1) = a(n) + a(n - n mod 2). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 26 2008
%p A038754 a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=3*a[n-2]+2 od: seq(a[n]+1, 
               n=0..34); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 
               2008
%o A038754 (PARI) a(n)=(1/6)*(5-(-1)^n)*3^floor(n/2)
%Y A038754 Cf. Somos sequences A006720, A006721, A006722, A006723.
%Y A038754 a(n) = A094718(5, n).
%Y A038754 Cf. A000079, A133464, A140730, A037124.
%Y A038754 Sequence in context: A035522 A018311 A018481 this_sequence A133626 A165647 
               A066313
%Y A038754 Adjacent sequences: A038751 A038752 A038753 this_sequence A038755 A038756 
               A038757
%K A038754 easy,nice,nonn
%O A038754 0,2
%A A038754 Henry Bottomley (se16(AT)btinternet.com), May 03 2000

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