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A052528
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Expansion of (1-x)/(1-2x-2x^2+2x^3).
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4
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1, 1, 4, 8, 22, 52, 132, 324, 808, 2000, 4968, 12320, 30576, 75856, 188224, 467008, 1158752, 2875072, 7133632, 17699904, 43916928, 108966400, 270366848, 670832640, 1664466176, 4129863936, 10246994944, 25424785408, 63083832832
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Form the graph with matrix A=[1,1,1,1;1,0,0,0;1,0,0,0;1,0,0,1]. Then A052528 counts closed walks of length n at the degree 5 vertex. - Paul Barry (pbarry(AT)wit.ie), Oct 02 2004
Equals the INVERT transform of (1, 3, 1, 1, 1,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 27 2009]
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 455
Index to sequences with linear recurrences with constant coefficients, signature (2,2,-2).
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FORMULA
| G.f.: -(-1+x)/(1-2*x-2*x^2+2*x^3)
Recurrence: {a(1)=1, a(0)=1, a(2)=4, 2*a(n)-2*a(n+1)-2*a(n+2)+a(n+3)=0}
Sum(-1/37*(-5+9*_alpha^2-12*_alpha)*_alpha^(-1-n), _alpha=RootOf(2*_Z^3-2*_Z^2-2*_Z+1))
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MAPLE
| spec := [S, {S=Sequence(Prod(Z, Union(Z, Z, Sequence(Z))))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
| Cf. A077937, A052987.
Sequence in context: A175655 A000639 A190795 * A058855 A057583 A129788
Adjacent sequences: A052525 A052526 A052527 * A052529 A052530 A052531
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 06 2000
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