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Search: id:A052906
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| A052906 |
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A simple regular expression. |
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+0
4
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| 1, 3, 9, 30, 99, 327, 1080, 3567, 11781, 38910, 128511, 424443, 1401840, 4629963, 15291729, 50505150, 166807179, 550926687, 1819587240, 6009688407, 19848652461, 65555645790, 216515589831, 715102415283, 2361822835680
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Image of 1/(1-3x) under the mapping g(x)->g(x/(1+x^2)). - Paul Barry (pbarry(AT)wit.ie), Jan 16 2005
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 885
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FORMULA
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G.f.: (-1+x^2)/(-1+3*x+x^2)
Recurrence: {a(0)=1, a(n)+3*a(n+1)-a(n+2), a(1)=3, a(2)=9}
Sum(-3/13*(3*_alpha-2)*_alpha^(-1-n), _alpha=RootOf(-1+3*_Z+_Z^2))
a(n)=sum{k=0..floor(n/2), binomial(n-k-1)3^(n-2k)} - Paul Barry (pbarry(AT)wit.ie), Jan 16 2005
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MAPLE
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spec := [S, {S=Sequence(Prod(Union(Z, Z, Z), Sequence(Prod(Z, Z))))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
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First differences are in A003688.
Sequence in context: A078844 A144817 A089978 this_sequence A102898 A050181 A089931
Adjacent sequences: A052903 A052904 A052905 this_sequence A052907 A052908 A052909
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 06 2000
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