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Search: id:A052533
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| A052533 |
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A simple regular expression. |
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+0
2
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| 1, 0, 3, 3, 12, 21, 57, 120, 291, 651, 1524, 3477, 8049, 18480, 42627, 98067, 225948, 520149, 1197993, 2758440, 6352419, 14627739, 33684996, 77568213, 178623201, 411327840, 947197443, 2181180963, 5022773292, 11566316181, 26634636057
(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;1,1,0,0;1,0,1,0;1,0,0,1]. A052533 counts closed walks of length n at the vertex without loop. - Paul Barry (pbarry(AT)wit.ie), Oct 02 2004
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 463
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FORMULA
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G.f.: (-1+x)/(-1+x+3*x^2)
Recurrence: {a(1)=0, a(0)=1, 3*a(n)+a(n+1)-a(n+2)}
Sum(1/13*(-1+7*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+3*_Z^2))
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MAPLE
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spec := [S, {S=Sequence(Prod(Z, Union(Z, Z, Z), Sequence(Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
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Cf. A006130.
Sequence in context: A075780 A078666 A006804 this_sequence A136533 A161804 A097342
Adjacent sequences: A052530 A052531 A052532 this_sequence A052534 A052535 A052536
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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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