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A162273
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a(n) = ((2+sqrt(3))*(3+sqrt(3))^n + (2-sqrt(3))*(3-sqrt(3))^n)/2.
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1
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2, 9, 42, 198, 936, 4428, 20952, 99144, 469152, 2220048, 10505376, 49711968, 235239552, 1113165504, 5267555712, 24926341248, 117952713216, 558158231808, 2641233111552, 12498449278464, 59143297001472, 279869086338048
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OFFSET
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0,1
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COMMENTS
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Binomial transform of A001075 without initial term 1, inverse binomial transform of A162274.
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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 > 1; a(0) = 2, a(1) = 9.
G.f.: (2-3*x)/(1-6*x+6*x^2).
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MAPLE
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seq(simplify(((2+sqrt(3))*(3+sqrt(3))^n+(2-sqrt(3))*(3-sqrt(3))^n)*1/2), n = 0 .. 22); # Emeric Deutsch, Jul 11 2009
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MATHEMATICA
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LinearRecurrence[{6, -6}, {2, 9}, 30] (* Harvey P. Dale, Dec 17 2019 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((2+r)*(3+r)^n+(2-r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 05 2009
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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), Jun 29 2009
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EXTENSIONS
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STATUS
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approved
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