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A056236
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(2+sqrt(2))^n+(2-sqrt(2))^n.
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5
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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
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..24.
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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).
a(n)=2^(2*n)*[cos(Pi/8)^(2*n)+cos(3*Pi/8)^2*n]; also, a(n)=3*a(n-1)+Sum{k=1..n-2} a(k), for n>1, with a(0)=2, a(1)=4. - L. Edson Jeffery, April 8, 2011.
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MATHEMATICA
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LinearRecurrence[{4, -2}, {2, 4}, 30] (* Harvey P. Dale, Jan 18 2013 *)
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PROG
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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: A126946 A113179 A214761 * A028329 A204678 A025227
Adjacent sequences: A056233 A056234 A056235 * 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, Aug 11 2000
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EXTENSIONS
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More terms from James A. Sellers, Aug 25 2000
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STATUS
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approved
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