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Search: id:A028495
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| A028495 |
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Expansion of (1-x^2)/(1-x-2*x^2+x^3). |
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+0
12
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| 1, 1, 2, 3, 6, 10, 19, 33, 61, 108, 197, 352, 638, 1145, 2069, 3721, 6714, 12087, 21794, 39254, 70755, 127469, 229725, 413908, 745889, 1343980, 2421850, 4363921, 7863641, 14169633, 25532994, 46008619, 82904974, 149389218, 269190547
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Form the graph with matrix A=[0,1,1;1,0,0;1,0,1] (P_3 with a loop at an extremity). Then A052547 counts closed walks of length n at the degree 3 vertex. - Paul Barry (pbarry(AT)wit.ie), Oct 02 2004
Equals INVERT transform of (1, 1, 0, 1, 0, 1, 0, 1,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 28 2009]
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1056
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1057
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FORMULA
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Recurrence: {a(1)=1, a(0)=1, a(2)=2, a(n)-2*a(n+1)-a(n+2)+a(n+3)}.
a(n) = Sum(1/7*(1+2*_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^3-2*_Z^2-_Z+1))
a(n)=5a(n-2)-6a(n-4)+a(n-6) - Floor van Lamoen (fvlamoen(AT)hotmail.com), Nov 02 2005
a(n)=a(n-1)+ SUM_{0<k<=n/2}a(n-2k) - Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 29 2005
a(n) = A006053(n+2)-A006053(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
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MAPLE
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spec := [S, {S=Sequence(Union(Prod(Sequence(Prod(Z, Z)), Z, Z), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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CROSSREFS
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a(n) = A094718(6, n).
Cf. A096976, A052547.
Sequence in context: A007473 A014595 A079959 this_sequence A136752 A093126 A003237
Adjacent sequences: A028492 A028493 A028494 this_sequence A028496 A028497 A028498
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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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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