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A154250
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a(n) = ( (9 + sqrt(7))^n - (9 - sqrt(7))^n )/(2*sqrt(7)).
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1
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1, 18, 250, 3168, 38524, 459000, 5411224, 63436032, 741418000, 8651257632, 100857705376, 1175245632000, 13690951178176, 159468944439168, 1857310612720000, 21630889140461568, 251915019187028224
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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(7) = 11.6457513110....
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LINKS
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FORMULA
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a(n) = 18*a(n-1) - 74*a(n-2) for n>1, with a(0)=0, a(1)=1.
G.f.: x/(1 - 18*x + 74*x^2). (End)
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MATHEMATICA
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LinearRecurrence[{18, -74}, {1, 18}, 20] (* Harvey P. Dale, Feb 16 2014 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-7); 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. A010465 (decimal expansion of square root of 7).
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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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