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A052911
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Expansion of (1-x)/(1-3x-x^2+2x^3).
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3
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1, 2, 7, 21, 66, 205, 639, 1990, 6199, 19309, 60146, 187349, 583575, 1817782, 5662223, 17637301, 54938562, 171128541, 533049583, 1660400166, 5171992999, 16110279997, 50182032658, 156312391973, 486898648583, 1516644272406
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 891
Index to sequences with linear recurrences with constant coefficients, signature (3,1,-2).
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FORMULA
| G.f.: -(-1+x)/(1-3*x-x^2+2*x^3)
Recurrence: {a(0)=1, a(1)=2, a(2)=7, 2*a(n)-a(n+1)-3*a(n+2)+a(n+3)=0}
Sum(-1/229*(-43-41*_alpha+46*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z-_Z^2+2*_Z^3))
a(n) = center term in M^n * [1 1 1] where M = Hosoya's triangle considered as an upper triangular 3 X 3 matrix: [2 1 2 / 1 1 0 / 1 0 0]. E.g. a(4) = 66 since M^4 * [1 1 1] = [139 66 45]. The analogous procedure using M^n * [1 0 0] generates A100058. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 31 2004
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MAPLE
| spec := [S, {S=Sequence(Union(Z, Prod(Union(Sequence(Z), Z, Z), Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
| Cf. A100058, A058071, A100059.
Sequence in context: A106271 A027990 A037520 * A126133 A186240 A127540
Adjacent sequences: A052908 A052909 A052910 * A052912 A052913 A052914
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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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