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A052907
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Expansion of 1/(1-2x^2-2x^3).
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4
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1, 0, 2, 2, 4, 8, 12, 24, 40, 72, 128, 224, 400, 704, 1248, 2208, 3904, 6912, 12224, 21632, 38272, 67712, 119808, 211968, 375040, 663552, 1174016, 2077184, 3675136, 6502400, 11504640, 20355072, 36014080, 63719424, 112738304, 199467008
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 887
Index to sequences with linear recurrences with constant coefficients, signature (0,2,2)
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FORMULA
| G.f.: -1/(-1+2*x^2+2*x^3)
Recurrence: {a(1)=0, a(0)=1, a(2)=2, 2*a(n)+2*a(n+1)-a(n+3)=0}
Sum(-1/19*(-3-5*_alpha+4*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z^2+2*_Z^3))
a(n)=2a(n-2)+2a(n-3); a(n)=sum{k=0..floor(n/2), binomial(k, n-2k)2^k}. - Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
a(n)=sum{k=0..floor(n/2), binomial(k, n-2k)2^k} - Paul Barry (pbarry(AT)wit.ie), Oct 19 2004
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MAPLE
| spec := [S, {S=Sequence(Prod(Union(Z, Z), Union(Z, Prod(Z, Z))))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
| LinearRecurrence[{0, 2, 2}, {1, 0, 2}, 50] (* From Harvey P. Dale, Oct 30 2011 *)
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CROSSREFS
| Sequence in context: A104221 A078044 A153993 * A048114 A102456 A032067
Adjacent sequences: A052904 A052905 A052906 * A052908 A052909 A052910
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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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