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A056236
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a(n) = (2 + sqrt(2))^n + (2 - sqrt(2))^n.
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10
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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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COMMENTS
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Binomial transform of A002203 [Bhadouria].
The binomial transform of this sequence is 2, 6, 22, 90, 386, .. = 2*A083878(n). - R. J. Mathar, Nov 10 2013
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LINKS
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FORMULA
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a(n) = 4*a(n-1) - 2*a(n-2).
a(n) = a(n-2) - a(n-1) + 2*A020727(n-1).
For n>2, a(n) = floor((2+sqrt(2))*a(n-1)).
G.f.: 2*(1-2*x)/(1-4*x+2*x^2).
a(n) = 2^(2*n)*(cos(Pi/8)^(2*n) + cos(3*Pi/8)^(2*n)).
a(n) = 3*a(n-1) + Sum_{k=1..(n-2)} a(k), for n>1, with a(0)=2, a(1)=4. (End)
a(n) = [x^n] ( (1 + 4*x + sqrt(1 + 8*x + 8*x^2))/2 )^n for n >= 1. - Peter Bala, Jun 23 2015
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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, Jun 25 2008
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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