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A143648
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a(n) = ((4 + sqrt 6)^n + (4 - sqrt 6)^n)/2.
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1
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1, 4, 22, 136, 868, 5584, 35992, 232096, 1496848, 9653824, 62262112, 401558656, 2589848128, 16703198464, 107727106432, 694784866816, 4481007870208, 28900214293504, 186391635645952, 1202130942232576, 7753131181401088
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A084120. Sequences defined by a(n) = ((A + sqrt(B))^n + (A - sqrt(B))^n)/2 have recurrences a(n) = 2*A*a(n-1) + (B - A^2)*a(n-2) and generating functions g.f.: (1-Ax)/(1-2Ax+(A^2-B)x^2). - R. J. Mathar, Nov 01 2008
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LINKS
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FORMULA
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a(n) = 8*a(n-1) - 10*a(n-2).
G.f.: (1-4x)/(1-8x+10x^2). (End)
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EXAMPLE
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a(3) = 136.
a(4) = ((4 + sqrt(6))^4 + (4 - sqrt(6))^4)/2 = 4^4 + 6*sqrt(6)^2*4^2 + sqrt(6)^4 = 4^4 + 6*6*4^2 + 6^2 = 868. - Klaus Brockhaus, Nov 01 2008
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MATHEMATICA
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PROG
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(Magma) Z<x>:= PolynomialRing(Integers()); N<r6>:=NumberField(x^2-6); S:=[ ((4+r6)^n+(4-r6)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 01 2008
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CROSSREFS
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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), Oct 27 2008
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EXTENSIONS
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STATUS
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approved
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