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A052937
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Expansion of (2-3x-x^2)/((1-x)(1-2x-x^2)).
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2
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2, 3, 6, 13, 30, 71, 170, 409, 986, 2379, 5742, 13861, 33462, 80783, 195026, 470833, 1136690, 2744211, 6625110, 15994429, 38613966, 93222359, 225058682, 543339721, 1311738122, 3166815963, 7645370046, 18457556053, 44560482150
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 928
Index to sequences with linear recurrences with constant coefficients, signature (3,-1,-1).
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FORMULA
| G.f.: -(-2+3*x+x^2)/(-1+x)/(-1+2*x+x^2)
Recurrence: {a(2)=6, a(1)=3, a(0)=2, -a(n)-2*a(n+1)+a(n+2)+2=0.}
1+Sum(1/4*(1+_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z+_Z^2))
a(n) = A000129(n+1)+1, where A000129 are the Pell Numbers. - Graeme McRae (g_m(AT)mcraefamily.com), Aug 03 2006
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MAPLE
| spec := [S, {S=Union(Sequence(Z), Sequence(Union(Z, Z, Prod(Z, Z))))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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CROSSREFS
| Cf. A001333.
Sequence in context: A107316 A124682 A079512 * A174191 A005554 A077212
Adjacent sequences: A052934 A052935 A052936 * A052938 A052939 A052940
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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 05 2000
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