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A052986
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Expansion of ( 1-2*x ) / ( (x-1)*(2*x^2+3*x-1) ).
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1
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1, 2, 7, 24, 85, 302, 1075, 3828, 13633, 48554, 172927, 615888, 2193517, 7812326, 27824011, 99096684, 352938073, 1257007586, 4476898903, 15944711880, 56787933445, 202253224094, 720335539171, 2565513065700, 9137210275441, 32542656957722, 115902391424047
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1-2*x)/(1-4*x+x^2+2*x^3).
Recurrence: {a(0)=1, a(1)=2, -2*a(n)-3*a(n+1)+a(n+2)+1=0}.
a(n) = Sum(-1/136*(-13-27*r+6*r^2)*r^(-1-n) where r=RootOf(1-4*_Z+_Z^2+2*_Z^3)).
a(n) = (1/4+(2^(-3-n)*((3-sqrt(17))^n*(-5+3*sqrt(17))+(3+sqrt(17))^n*(5+3*sqrt(17))))/sqrt(17)). - Colin Barker, Sep 02 2016
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MAPLE
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spec := [S, {S=Sequence(Union(Prod(Union(Sequence(Union(Z, Z)), Z), Z), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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MATHEMATICA
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PROG
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(Magma) I:=[1, 2, 7]; [n le 3 select I[n] else 4*Self(n-1)-Self(n-2)-2*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 23 2012
(PARI) a(n) = round((1/4+(2^(-3-n)*((3-sqrt(17))^n*(-5+3*sqrt(17))+(3+sqrt(17))^n*(5+3*sqrt(17))))/sqrt(17))) \\ Colin Barker, Sep 02 2016
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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STATUS
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approved
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