Search: id:A057682
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%I A057682
%S A057682 0,1,2,3,3,0,9,27,54,81,81,0,243,729,1458,2187,2187,0,6561,19683,
%T A057682 39366,59049,59049,0,177147,531441,1062882,1594323,1594323,0,4782969,
%U A057682 14348907,28697814,43046721,43046721,0,129140163,387420489,774840978
%V A057682 0,1,2,3,3,0,-9,-27,-54,-81,-81,0,243,729,1458,2187,2187,0,-6561,-19683,
%W A057682 -39366,-59049,-59049,0,177147,531441,1062882,1594323,1594323,0,-4782969,
%X A057682 -14348907,-28697814,-43046721,-43046721,0,129140163,387420489,774840978
%N A057682 Sum((-1)^j*binomial(n,3*j+1),j=0..floor(n/3)).
%F A057682 Starting at 1, the binomial transform of A000484. - Paul Barry (pbarry(AT)wit.ie), 
               Jul 21 2003
%F A057682 It appears that Abs[a(n)]=Floor[Abs[A000748(n)]/3]. - John W. Layman 
               (layman(AT)math.vt.edu), Sep 05 2003
%F A057682 a(n)={(3+i*sqrt(3))/2}^(n-2)+{(3-i*sqrt(3))/2}^(n-2) - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Oct 27 2003
%F A057682 G.f.:(x-x^2)/(1-3*x+3*x^2). a(n)=3*a(n-1)-3*a(n-2), if n>1.
%o A057682 (PARI) a(n)=sum(j=0,n\3,(-1)^j*binomial(n,3*j+1)) /* Michael Somos May 
               26 2004 */
%o A057682 (PARI) a(n)=if(n<2,n>0,n-=2; polsym(x^2-3*x+3,n)[n+1]) /* Michael Somos 
               May 26 2004 */
%Y A057682 Alternating row sums of triangle A030523.
%Y A057682 Sequence in context: A106242 A121474 A138003 this_sequence A124841 A085355 
               A103120
%Y A057682 Adjacent sequences: A057679 A057680 A057681 this_sequence A057683 A057684 
               A057685
%K A057682 sign
%O A057682 0,3
%A A057682 N. J. A. Sloane (njas(AT)research.att.com), Oct 20 2000

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