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Search: id:A056236
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| A056236 |
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(2+sqrt(2))^n+(2-sqrt(2))^n. |
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+0
4
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| 2, 4, 12, 40, 136, 464, 1584, 5408, 18464, 63040, 215232, 734848, 2508928, 8566016, 29246208, 99852800, 340918784, 1163969536, 3974040576, 13568223232, 46324811776, 158162800640, 540001579008, 1843680714752, 6294719700992
(list; graph; listen)
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OFFSET
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0,1
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FORMULA
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a(n) = 4*a(n-1)-2*a(n-2) = a(n-2)-a(n-1)+2*A020727(n-1) = 2*A006012(n) = 4*A007052(n-1). For n>2, a(n) = floor[(2+sqrt(2))*a(n-1)].
G.f.: (2-4x)/(1-4x+2x^2).
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PROGRAM
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(PARI) a(n)=2*real((2+quadgen(8))^n)
sage: [lucas_number2(n, 4, 2) for n in range(37)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008
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CROSSREFS
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Sequence in context: A099214 A126946 A113179 this_sequence A028329 A025227 A119430
Adjacent sequences: A056233 A056234 A056235 this_sequence A056237 A056238 A056239
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KEYWORD
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nonn,easy
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Aug 11 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 25 2000
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