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A052927
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Expansion of 1/(1-4x-x^3).
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0
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1, 4, 16, 65, 264, 1072, 4353, 17676, 71776, 291457, 1183504, 4805792, 19514625, 79242004, 321773808, 1306609857, 5305681432, 21544499536, 87484608001, 355244113436, 1442520953280, 5857568421121, 23785517797920, 96584592144960, 392195937000961
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A transform of A000302 under the mapping mapping g(x)->(1/(1-x^3))g(x/(1-x^3)). - Paul Barry (pbarry(AT)wit.ie), Oct 20 2004
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 913
Index to sequences with linear recurrences with constant coefficients, signature (4,0,1).
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FORMULA
| G.f.: -1/(-1+4*x+x^3)
Recurrence: {a(0)=1, a(1)=4, a(2)=16, a(n)+4*a(n+2)-a(n+3)=0}
Sum(1/283*(64+24*_alpha^2+9*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+4*_Z+_Z^3))
a(n)=sum{k=0..floor(n/3), binomial(n-2k, k)4^(n-3k)}. - Paul Barry (pbarry(AT)wit.ie), Oct 20 2004
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MAPLE
| spec := [S, {S=Sequence(Union(Z, Z, Z, Z, Prod(Z, Z, Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
| CoefficientList[Series[1/(1-4x-x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{4, 0, 1}, {1, 4, 16}, 40] (* From Vladimir Joseph Stephan Orlovsky, Jan 28 2012 *)
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CROSSREFS
| Cf. A099503.
Sequence in context: A175065 A033140 A181879 * A012781 A132820 A165201
Adjacent sequences: A052924 A052925 A052926 * A052928 A052929 A052930
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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