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A162560
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a(n) = (4+sqrt(3))*(3+sqrt(3))^n + (4-sqrt(3))*(3-sqrt(3))^n.
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1
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3, 8, 30, 132, 612, 2880, 13608, 64368, 304560, 1441152, 6819552, 32270400, 152705088, 722608128, 3419418240, 16180860672, 76568654592, 362326763520, 1714548653568, 8113331340288, 38392696120320, 181676188680192
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OFFSET
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-1,1
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COMMENTS
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Equals b(k) = ((9+sqrt(3))*(3-sqrt(3))^k+(9-sqrt(3))*(3+sqrt(3))^k)/6 for k >= 0. - Klaus Brockhaus, Jul 14 2009
Third binomial transform of A162852.
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LINKS
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FORMULA
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a(n) = 6*a(n-1) - 6*a(n-2) for n > 0; a(-1) = 3, a(0) = 8.
G.f.: (3-10*x)/(x*(1-6*x+6*x^2)).
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((4+r)*(3+r)^n+(4-r)*(3-r)^n): n in [-1..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 14 2009
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CROSSREFS
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Cf. A162852 (3, -1, 9, -3, 27, -9, 81, ...).
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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), Jul 06 2009
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EXTENSIONS
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STATUS
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approved
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