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Search: id:A090965
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| A090965 |
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a(0) = 1, a(1) = 4, a(n+1) = 8a(n) - 4a(n-1). |
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+0
9
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| 1, 4, 28, 208, 1552, 11584, 86464, 645376, 4817152, 35955712, 268377088, 2003193856, 14952042496, 111603564544, 833020346368, 6217748512768, 46409906716672, 346408259682304, 2585626450591744, 19299378566004736
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sum_{k>=0} A086645(n,k)*m^k for m = 0, 1, 2, 4 gives A000007, A081294, A001541, A083884.
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FORMULA
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a(n) = Sum_{k>=0} binomial(2n, 2k)*3^k = Sum_{k>=0} A086645(n, k)*3^k . a(n) = 2^n*A001075(n).
a(n)=1/2*{[4-2*sqrt(3)]^n+[4+2*sqrt(3)]^n}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 20 2008]
G.f.:(1-4x)/(1-8x+4x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 07 2009]
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PROGRAM
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sage: [lucas_number2(n, 8, 4)/2 for n in xrange(0, 21)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2008
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CROSSREFS
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Sequence in context: A155611 A002903 A019482 this_sequence A106258 A085363 A039741
Adjacent sequences: A090962 A090963 A090964 this_sequence A090966 A090967 A090968
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KEYWORD
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easy,nonn
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AUTHOR
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DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 29 2004
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
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