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Search: id:A144844
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| A144844 |
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((2+sqrt2)^n-(2-sqrt2)^n)^2/8 |
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+0
1
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| 0, 1, 16, 196, 2304, 26896, 313600, 3655744, 42614784, 496754944, 5790601216, 67500196864, 786839961600, 9172078759936, 106917585289216, 1246322708463616, 14528202160472064, 169353135091941376, 1974124812461670400, 23012085209172803584
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: x(1+2x)/((1-2x)(1-12x+4x^2)). a(n)=2^(n-2)*(A001109(n+1)-3*A001109(n)-1) = 2^(n-1)*A001108(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 24 2008]
a(n) = 14*a(n-1)-28*a(n-2)+8*a(n-3) for n > 2; a(0) = 0, a(1) = 1; a(2) = 16. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 15 2009]
a(n) = A007070(n)^2 = (((sqrt(2)+1)^n - (sqrt(2)-1)^n)) / 2) ^ 2. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 06 2009]
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MATHEMATICA
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Table[ Simplify[ ((2 + Sqrt@2)^n - (2 - Sqrt@2)^n)^2/8], {n, 0, 19}] (* Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 24 2008 *)
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r2>:=NumberField(x^2-2); [ Integers()!a: a in [ ((2+r2)^n-(2-r2)^n)^2/8: n in [0..19] ] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 20 2008]
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CROSSREFS
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Sequence in context: A016173 A005747 A103721 this_sequence A093060 A153885 A016226
Adjacent sequences: A144841 A144842 A144843 this_sequence A144845 A144846 A144847
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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), Sep 22 2008
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 24 2008
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