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Search: id:A164535
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| A164535 |
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a(n) = ((3+4*sqrt(2))*(4+sqrt(2))^n+(3-4*sqrt(2))*(4-sqrt(2))^n)/2. |
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+0
3
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| 3, 20, 118, 664, 3660, 19984, 108632, 589280, 3193392, 17297216, 93670240, 507200896, 2746223808, 14868977920, 80504690048, 435871829504, 2359908975360, 12777066189824, 69177803863552, 374543504250880
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OFFSET
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0,1
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COMMENT
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Binomial transform of A164305. Fourth binomial transform of A164654. Inverse binomial transform of A164536.
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FORMULA
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a(n) = 8*a(n-1)-14*a(n-2) for n > 1; a(0) = 3, a(1) = 20.
G.f.: (3-4*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:=[ ((3+4*r)*(4+r)^n+(3-4*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 20 2009]
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CROSSREFS
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Cf. A164305, A164654, A164536.
Sequence in context: A154641 A108911 A005096 this_sequence A001652 A128910 A037788
Adjacent sequences: A164532 A164533 A164534 this_sequence A164536 A164537 A164538
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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 15 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 20 2009
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