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A080877
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a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=1, a(2)=2.
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6
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1, 1, 2, 3, 8, 14, 40, 72, 208, 376, 1088, 1968, 5696, 10304, 29824, 53952, 156160, 282496, 817664, 1479168, 4281344, 7745024, 22417408, 40553472, 117379072, 212340736, 614604800, 1111830528, 3218112512, 5821620224, 16850255872
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: (-3*x^3 - 4*x^2 + x + 1)/(4*x^4 - 6*x^2 + 1)
a(n) = ( - 1/20*5^(1/2) + 1/16*5^(1/2)*2^(1/2) - 1/16*2^(1/2) + 1/4)*(sqrt(3 + sqrt(5)))^n + (1/20*5^(1/2) + 1/16*5^(1/2)*2^(1/2) + 1/16*2^(1/2) + 1/4)*(sqrt(3 - sqrt(5)))^n + ( - 1/20*5^(1/2) - 1/16*5^(1/2)*2^(1/2) + 1/16*2^(1/2) + 1/4)*( - (sqrt(3 + sqrt(5))))^n + (1/20*5^(1/2) - 1/16*5^(1/2)*2^(1/2) - 1/16*2^(1/2) + 1/4)*( - (sqrt(3 - sqrt(5))))^n [From Richard Choulet, Dec 07 2008]
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MATHEMATICA
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LinearRecurrence[{0, 6, 0, -4}, {1, 1, 2, 3}, 50] (* or *) CoefficientList[ Series[ (-3x^3-4x^2+x+1)/(4x^4-6x^2+1), {x, 0, 50}], x] (* Harvey P. Dale, May 02 2011 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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