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A052954
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Expansion (2-x-x^2-x^3)/((1-x)(1-x^2-x^3)).
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0
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2, 1, 2, 2, 2, 3, 3, 4, 5, 6, 8, 10, 13, 17, 22, 29, 38, 50, 66, 87, 115, 152, 201, 266, 352, 466, 617, 817, 1082, 1433, 1898, 2514, 3330, 4411, 5843, 7740, 10253, 13582, 17992, 23834, 31573, 41825, 55406, 73397, 97230, 128802, 170626, 226031, 299427
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| For n>2 a(n) = floor{sqrt(a(n-3)*a(n-2) + a(n-2)*a(n-1) + a(n-1)*a(n-3))} - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Sep 19 2004
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1025
Index to sequences with linear recurrences with constant coefficients, signature (1,1,0,-1)
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FORMULA
| G.f.: -(-2+x+x^2+x^3)/(-1+x^2+x^3)/(-1+x)
Recurrence: {a(1)=1, a(2)=2, a(3)=2, a(0)=2, -a(n)-a(n+1)+1+a(n+3)=0}
1+Sum(-1/23*(-3-7*_alpha+2*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(_Z^3+_Z^2-1))
lim n->inf a(n)/a(n-1) = positive root of 1+x-x^3 (smallest Pisot-Vijayaraghavan number, A060006) - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Sep 19 2004
a(n) = 2*A023434(n+1)-A023434(n)-A023434(n-2)-A023434(n-3). - R. J. Mathar, Nov 28 2011
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MAPLE
| spec := [S, {S=Union(Sequence(Prod(Union(Prod(Z, Z), Z), Z)), Sequence(Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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CROSSREFS
| Cf. A060006 A023434.
Sequence in context: A084840 A029278 A125950 * A123505 A114920 A030361
Adjacent sequences: A052951 A052952 A052953 * A052955 A052956 A052957
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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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