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A057682
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Sum((-1)^j*binomial(n,3*j+1),j=0..floor(n/3)).
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5
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0, 1, 2, 3, 3, 0, -9, -27, -54, -81, -81, 0, 243, 729, 1458, 2187, 2187, 0, -6561, -19683, -39366, -59049, -59049, 0, 177147, 531441, 1062882, 1594323, 1594323, 0, -4782969, -14348907, -28697814, -43046721, -43046721, 0, 129140163, 387420489, 774840978
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f.: (x-x^2)/(1-3*x+3*x^2).
a(n)=3*a(n-1)-3*a(n-2), if n>1.
Starting at 1, the binomial transform of A000484. - Paul Barry (pbarry(AT)wit.ie), Jul 21 2003
It appears that Abs[a(n)]=Floor[Abs[A000748(n)]/3]. - John W. Layman (layman(AT)math.vt.edu), Sep 05 2003
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
a(n) = n*hypergeom([1/3-n/3,2/3-n/3,1-n/3],[2/3,4/3],1) for n>=1. [From John M. Campbell, June 1, 2011]
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MATHEMATICA
| Table[n*HypergeometricPFQ[{1/3 - n/3, 2/3 - n/3, 1 - n/3}, {2/3, 4/3}, 1], {n, 1, 40}] [ * From John M. Campbell, June 1, 2011 * ]
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PROG
| (PARI) a(n)=sum(j=0, n\3, (-1)^j*binomial(n, 3*j+1)) /* Michael Somos May 26 2004 */
(PARI) a(n)=if(n<2, n>0, n-=2; polsym(x^2-3*x+3, n)[n+1]) /* Michael Somos May 26 2004 */
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CROSSREFS
| Alternating row sums of triangle A030523.
Sequence in context: A106242 A121474 A138003 * A124841 A085355 A103120
Adjacent sequences: A057679 A057680 A057681 * A057683 A057684 A057685
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Oct 20 2000
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