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Search: id:A090017
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| A090017 |
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a(n) = 4a(n-1) + 2a(n-2), a(0) = 0, a(1) = 1. |
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+0
3
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| 0, 1, 4, 18, 80, 356, 1584, 7048, 31360, 139536, 620864, 2762528, 12291840, 54692416, 243353344, 1082798208, 4817899520, 21437194496, 95384577024, 424412697088, 1888419942400, 8402505163776, 37386860539904, 166352452487168
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n) = (-i*sqrt(2))^(n-1) U(n-1, i*sqrt(2)) where U is the Chebyshev polynomial of the second kind and i^2 = -1.
a(n) = ((2+sqrt(6))^n - (2-sqrt(6))^n)/(2 sqrt(6)). [From Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009, Jan 07 2009]
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MATHEMATICA
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a[n_Integer] := (-I Sqrt[2])^(n - 1) ChebyshevU[ n - 1, I Sqrt[2] ]
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PROGRAM
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(Sage) [lucas_number1(n, 4, -2) for n in xrange(0, 23)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
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Cf. A007070, A084059.
Sequence in context: A112619 A037965 A045902 this_sequence A104631 A106391 A063881
Adjacent sequences: A090014 A090015 A090016 this_sequence A090018 A090019 A090020
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Nov 19 2003
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EXTENSIONS
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Edited by Stuart Clary, Oct 25 2009
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