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Search: id:A052544
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| A052544 |
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A simple regular expression. |
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+0
3
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| 1, 2, 6, 19, 60, 189, 595, 1873, 5896, 18560, 58425, 183916, 578949, 1822473, 5736961, 18059374, 56849086, 178955183, 563332848, 1773314929, 5582216355, 17572253481, 55315679788, 174128175064, 548137914373, 1725482812088
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Equals INVERT transform of (1, 1, 3, 8, 21, 55, 144,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 01 2009]
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 480
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FORMULA
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G.f.: -(-1+x)^2/(-1+4*x-3*x^2+x^3)
Recurrence: {a(0)=1, a(1)=2, a(2)=6, a(n)-3*a(n+1)+4*a(n+2)-a(n+3)}
Sum(-1/31*(-4-7*_alpha+2*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(-1+4*_Z-3*_Z^2+_Z^3))
a(n) = Sum(binomial(n+2k, 3k), {k=0...n}) - Richard Ollerton (r.ollerton(AT)uws.edu.au), May 12 2004
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MAPLE
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spec := [S, {S=Sequence(Union(Z, Prod(Z, Sequence(Z), Sequence(Z))))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
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Sequence in context: A111277 A014346 A118364 this_sequence A001169 A022041 A018906
Adjacent sequences: A052541 A052542 A052543 this_sequence A052545 A052546 A052547
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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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