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A164303
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a(n) = 2*a(n-1) + a(n-2) for n > 1; a(0) = 3, a(1) = 11.
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3
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3, 11, 25, 61, 147, 355, 857, 2069, 4995, 12059, 29113, 70285, 169683, 409651, 988985, 2387621, 5764227, 13916075, 33596377, 81108829, 195814035, 472736899, 1141287833, 2755312565, 6651912963, 16059138491, 38770189945, 93599518381
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = 2*a(n-1)+a(n-2) for n > 1; a(0) = 3, a(1) = 11.
a(n) = ((3+4*sqrt(2))*(1+sqrt(2))^n + (3-4*sqrt(2))*(1-sqrt(2))^n)/2.
G.f.: (3+5*x)/(1-2*x-x^2).
E.g.f.: (3*cosh(sqrt(2)*x) + 4*sqrt(2)*sinh(sqrt(2)*x))*exp(x). - G. C. Greubel, Sep 13 2017
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MATHEMATICA
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LinearRecurrence[{2, 1}, {3, 11}, 50] (* or *) CoefficientList[Series[(3 + 5*x)/(1 - 2*x - x^2), {x, 0, 50}], x] (* 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)*(1+r)^n+(3-4*r)*(1-r)^n)/2: n in [0..28] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009
(PARI) x='x+O('x^50); Vec((3+5*x)/(1-2*x-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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