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Search: id:A052921
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| A052921 |
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A simple regular expression. |
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+0
7
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| 1, 2, 4, 9, 21, 49, 114, 265, 616, 1432, 3329, 7739, 17991, 41824, 97229, 226030, 525456, 1221537, 2839729, 6601569, 15346786, 35676949, 82938844, 192809420, 448227521, 1042002567, 2422362079, 5631308624, 13091204281, 30433357674
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 905
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FORMULA
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G.f.: (-1+x)/(-1+3*x-2*x^2+x^3)
Recurrence: {a(0)=1, a(2)=4, a(1)=2, a(n)-2*a(n+1)+3*a(n+2)-a(n+3)}
Sum(1/23*(8-5*_alpha+7*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(-1+3*_Z-2*_Z^2+_Z^3))
Binomial transform of the Padovan sequence A000931(n+5). a(n)=sum{k=0..n+1, C(n+k+1, n-2k)}. - Paul Barry (pbarry(AT)wit.ie), Jun 21 2004
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MAPLE
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spec := [S, {S=Sequence(Union(Z, Z, Prod(Sequence(Z), Z, Z, Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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a=-1; b=0; c=1; lst={}; Do[AppendTo[lst, a+=b]; b+=c; c+=a, {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 20 2009]
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CROSSREFS
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Cf. A034943.
Cf. A097550, A137531 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 20 2009]
Sequence in context: A051164 A101891 A119967 this_sequence A018905 A024537 A027826
Adjacent sequences: A052918 A052919 A052920 this_sequence A052922 A052923 A052924
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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 05 2000
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