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A052993
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a(n)=a(n-1)+3a(n-2)-3a(n-3).
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0
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1, 1, 4, 4, 13, 13, 40, 40, 121, 121, 364, 364, 1093, 1093, 3280, 3280, 9841, 9841, 29524, 29524, 88573, 88573, 265720, 265720, 797161, 797161, 2391484, 2391484, 7174453, 7174453, 21523360, 21523360, 64570081, 64570081, 193710244
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1069
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FORMULA
| G.f.: 1/((-1+3*x^2)*(-1+x)).
Recurrence: {a(1)=1, a(0)=1, -3*a(n)-1+a(n+2)}
-1/2+Sum((1/4)*(1+3*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+3*_Z^2))
a(n)=sum{k=0..n, 3^(k/2)(1-(-1)^k)/(2sqrt(3))} - Paul Barry (pbarry(AT)wit.ie), Jul 28 2004
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MAPLE
| spec := [S, {S=Prod(Sequence(Prod(Union(Z, Z, Z), Z)), Sequence(Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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CROSSREFS
| Cf. A062318.
Sequence in context: A183362 A088838 A127403 * A005301 A099924 A147824
Adjacent sequences: A052990 A052991 A052992 * A052994 A052995 A052996
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 06 2000
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