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A163350
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a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 6.
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4
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1, 6, 34, 188, 1028, 5592, 30344, 164464, 890896, 4824672, 26124832, 141453248, 765878336, 4146681216, 22451153024, 121555687168, 658129355008, 3563255219712, 19292230787584, 104452273224704, 565526954771456
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A102285. Fourth binomial transform of A163403. Inverse binomial transform of A163346.
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LINKS
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FORMULA
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a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 6.
a(n) = ((1+sqrt(2))*(4+sqrt(2))^n+(1-sqrt(2))*(4-sqrt(2))^n)/2.
G.f.: (1-2*x)/(1-8*x+14*x^2).
E.g.f.: exp(4*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 19 2016
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MATHEMATICA
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LinearRecurrence[{8, -14}, {1, 6}, 30] (* Harvey P. Dale, May 08 2014 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+r)*(4+r)^n+(1-r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 26 2009
(PARI) Vec((1-2*x)/(1-8*x+14*x^2) + O(x^50)) \\ G. C. Greubel, Dec 19 2016
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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), Jul 25 2009
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EXTENSIONS
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STATUS
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approved
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