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A154241
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a(n) = ( (9 + sqrt(6))^n - (9 - sqrt(6))^n )/(2*sqrt(6)).
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1
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1, 18, 249, 3132, 37701, 443718, 5159349, 59589432, 685658601, 7872647418, 90283258449, 1034650095732, 11852457339501, 135745474931118, 1554484248297549, 17799805849522032, 203810186669080401
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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) = 9 + sqrt(6) = 11.4494897427....
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LINKS
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FORMULA
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a(n) = 18*a(n-1) - 75*a(n-2) for n>1, with a(0)=0, a(1)=1.
G.f.: x/(1 - 18*x + 75*x^2). (End)
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MATHEMATICA
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LinearRecurrence[{18, -75}, {1, 18}, 25] (* or *) Table[( (9 + sqrt(6))^n - (9 - sqrt(6))^n )/(2*sqrt(6)), {n, 1, 25}] (* G. C. Greubel, Sep 07 2016 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-6); S:=[ ((9+r)^n-(9-r)^n)/(2*r): n in [1..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009
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CROSSREFS
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Cf. A010464 (decimal expansion of square root of 6).
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KEYWORD
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nonn
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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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