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A164304
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a(n) = 4*a(n-1) - 2*a(n-2) for n > 1; a(0) = 3, a(1) = 14.
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3
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3, 14, 50, 172, 588, 2008, 6856, 23408, 79920, 272864, 931616, 3180736, 10859712, 37077376, 126590080, 432205568, 1475642112, 5038157312, 17201345024, 58729065472, 200513571840, 684596156416, 2337357481984, 7980237615104
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OFFSET
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0,1
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COMMENTS
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Binomial transform of A164303. Second binomial transform of A164654. Inverse binomial transform of A164305.
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LINKS
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FORMULA
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a(n) = 4*a(n-1) - 2*a(n-2) for n > 1; a(0) = 3, a(1) = 14.
a(n) = ((3+4*sqrt(2))*(2+sqrt(2))^n + (3-4*sqrt(2))*(2-sqrt(2))^n)/2.
G.f.: (3+2*x)/(1-4*x+2*x^2).
E.g.f.: (3*cosh(sqrt(2)*x) + 4*sqrt(2)*sinh(sqrt(2)*x))*exp(2*x). - G. C. Greubel, Sep 13 2017
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MATHEMATICA
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LinearRecurrence[{4, -2}, {3, 14}, 50] (* G. C. Greubel, Sep 13 2017 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+4*r)*(2+r)^n+(3-4*r)*(2-r)^n)/2: n in [0..24] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009
(PARI) x='x+O('x^50); Vec((3+2*x)/(1-4*x+2*x^2)) \\ G. C. Greubel, Sep 13 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Aug 12 2009
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EXTENSIONS
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STATUS
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approved
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