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A152055
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a(n) = ((8 + sqrt(3))^n + (8 - sqrt(3))^n)/2.
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1
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1, 8, 67, 584, 5257, 48488, 455131, 4324328, 41426257, 399036104, 3857575987, 37380013448, 362768079961, 3524108459048, 34256882467147, 333139503472424, 3240562225062817, 31527485889187208, 306765478498163491
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 16*a(n-1) - 61*a(n-2), n > 1; a(0)=1, a(1)=8.
G.f.: (1-8*x)/(1-16x+61*x^2).
a(n) = (Sum_{k=0..n} A098158(n,k)*8^(2*k)*3^(n-k))/8^n. (End)
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MATHEMATICA
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LinearRecurrence[{16, -61}, {1, 8}, 30] (* Harvey P. Dale, Sep 02 2018 *)
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PROG
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(Magma) Z<x>:= PolynomialRing(Integers()); N<r3>:=NumberField(x^2-3); S:=[ ((8+r3)^n+(8-r3)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 26 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), Nov 22 2008
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EXTENSIONS
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STATUS
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approved
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