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A154248
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a(n) = ( (7 + sqrt(7))^n - (7 - sqrt(7))^n )/(2*sqrt(7)).
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2
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1, 14, 154, 1568, 15484, 150920, 1462552, 14137088, 136492048, 1317130976, 12707167648, 122580846080, 1182430803904, 11405635719296, 110016806306176, 1061198588076032, 10236074368205056, 98734700455677440
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OFFSET
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1,2
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COMMENTS
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Lim_{n -> infinity} a(n)/a(n-1) = 7 + sqrt(7) = 9.6457513110....
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LINKS
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FORMULA
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a(n) = 14*a(n-1) - 42*a(n-2) for n>1, with a(0)=0, a(1)=1.
G.f.: x/(1 - 14x + 42x^2). (End)
E.g.f.: (1/sqrt(7))*exp(7*x)*sinh(sqrt(7)*x). - G. C. Greubel, Sep 08 2016
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MAPLE
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a:= n-> (<<0|1>, <-42|14>>^n)[1, 2]:
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MATHEMATICA
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LinearRecurrence[{14, -42}, {1, 14}, 25] (* or *) Table[( (7 + sqrt(7))^n - (7 - sqrt(7))^n )/(2*sqrt(7)), {n, 1, 25}] (* G. C. Greubel, Sep 08 2016 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-7); S:=[ ((7+r)^n-(7-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009
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CROSSREFS
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Cf. A010465 (decimal expansion of square root of 7).
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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), Jan 05 2009
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EXTENSIONS
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STATUS
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approved
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