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A152264
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a(n) = ((9+sqrt(6))^n + (9-sqrt(6))^n)/2.
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2
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1, 9, 87, 891, 9513, 104409, 1165887, 13155291, 149353713, 1701720009, 19429431687, 222100769691, 2540606477913, 29073358875609, 332774973917487, 3809447614844091, 43611934023382113, 499306241307571209
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 18*a(n-1) - 75*a(n-2), n > 1; a(0)=1, a(1)=9.
G.f.: (1-9*x)/(1-18*x+75*x^2).
a(n) = Sum_{k=0..n} A098158(n,k)*9^(2k-n)*6^(n-k). (End)
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MATHEMATICA
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CoefficientList[Series[(1-9x)/(1-18x+75x^2), {x, 0, 20}], x] (* or *) LinearRecurrence[{18, -75}, {1, 9}, 20] (* Harvey P. Dale, Feb 07 2023 *)
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PROG
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(Magma) Z<x>:= PolynomialRing(Integers()); N<r6>:=NumberField(x^2-6); S:=[ ((9+r6)^n+(9-r6)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 03 2008
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CROSSREFS
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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), Dec 01 2008
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EXTENSIONS
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STATUS
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approved
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