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Search: id:A164300
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| A164300 |
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a(n) = ((1+4*sqrt(2))*(4+sqrt(2))^n + (1-4*sqrt(2))*(4-sqrt(2))^n)/2. |
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+0
3
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| 1, 12, 82, 488, 2756, 15216, 83144, 452128, 2453008, 13294272, 72012064, 389976704, 2111644736, 11433484032, 61904845952, 335169991168, 1814692086016, 9825156811776, 53195565289984, 288012326955008
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OFFSET
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0,2
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COMMENT
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Binomial transform of A164299. Fourth binomial transform of A164587. Inverse binomial transform of A164301.
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FORMULA
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a(n) = 8*a(n-1)-14*a(n-2) for n > 1; a(0) = 1, a(1) = 12.
G.f.: (1+4*x)/(1-8*x+14*x^2).
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+4*r)*(4+r)^n+(1-4*r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 17 2009]
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CROSSREFS
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Cf. A164299, A164587, A164301.
Sequence in context: A007010 A069996 A163020 this_sequence A175037 A102105 A026949
Adjacent sequences: A164297 A164298 A164299 this_sequence A164301 A164302 A164303
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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), Aug 12 2009
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EXTENSIONS
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Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 17 2009
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