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A052941
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Expansion of (1-x)/(1-4x+x^2+x^3).
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0
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1, 3, 11, 40, 146, 533, 1946, 7105, 25941, 94713, 345806, 1262570, 4609761, 16830668, 61450341, 224360935, 819162731, 2990839648, 10919834926, 39869337325, 145566674726, 531477526653, 1940474094561, 7084852176865
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = term (3,1) in M^n, M = the 3x3 matrix [1,1,2; 1,2,1; 1,1,1]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 12 2009]
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 932
Index to sequences with linear recurrences with constant coefficients, signature (4,-1,-1).
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FORMULA
| G.f.: -(-1+x)/(1-4*x+x^2+x^3)
Recurrence: {a(0)=1, a(1)=3, a(n)+a(n+1)-4*a(n+2)+a(n+3)=0, a(2)=11}
Sum(-1/13*(_alpha^2-3)*_alpha^(-1-n), _alpha=RootOf(1-4*_Z+_Z^2+_Z^3))
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MAPLE
| spec := [S, {S=Sequence(Union(Z, Z, Prod(Union(Sequence(Z), Z), Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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CROSSREFS
| Sequence in context: A136775 A010911 A108153 * A014301 A119375 A149063
Adjacent sequences: A052938 A052939 A052940 * A052942 A052943 A052944
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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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