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Search: id:A164540
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| A164540 |
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a(n) = ((1+3*sqrt(2))*(2+2*sqrt(2))^n+(1-3*sqrt(2))*(2-2*sqrt(2))^n)/2. |
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+0
3
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| 1, 14, 60, 296, 1424, 6880, 33216, 160384, 774400, 3739136, 18054144, 87173120, 420909056, 2032328704, 9812951040, 47381118976, 228776280064, 1104629596160, 5333623504896, 25753012404224, 124346543636480, 600398224162816
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OFFSET
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0,2
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COMMENT
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Binomial transform of A164539. Second binomial transform of A164675. Inverse binomial transform of A164541.
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FORMULA
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a(n) = 4*a(n-1)+4*a(n-2) for n > 1; a(0) = 1, a(1) = 14.
G.f.: (1+10*x)/(1-4*x-4*x^2).
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(2+2*r)^n+(1-3*r)*(2-2*r)^n)/2: n in [0..21] ]; [ 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. A164539, A164675, A164541.
Sequence in context: A100171 A063492 A051799 this_sequence A140184 A025415 A125849
Adjacent sequences: A164537 A164538 A164539 this_sequence A164541 A164542 A164543
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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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