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A080872
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a(n)*a(n+3) - a(n+1)*a(n+2) = 4, given a(0)=a(1)=1, a(2)=5.
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4
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1, 1, 5, 9, 49, 89, 485, 881, 4801, 8721, 47525, 86329, 470449, 854569, 4656965, 8459361, 46099201, 83739041, 456335045, 828931049, 4517251249, 8205571449, 44716177445, 81226783441, 442644523201, 804062262961, 4381729054565
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..26.
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FORMULA
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G.f.: (-x^3 - 5*x^2 + x + 1)/(x^4 - 10*x^2 + 1)
a(n)=(3+sqrt(3))/12*(sqrt(3)-sqrt(2))^n+(3-sqrt(3))/12*(-sqrt(3)+sqrt(2))^n+(3+sqrt(3))/12*(sqrt(3)+sqrt(2))^n+(3-sqrt(3))/12*(-sqrt(3)-sqrt(2))^n [From Richard Choulet, Dec 03 2008]
a(n+4)=10*a(n+2)-a(n) [From Richard Choulet, Dec 04 2008]
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MATHEMATICA
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CoefficientList[Series[(-x^3-5 x^2+x+1)/(x^4-10 x^2+1), {x, 0, 30}], x] (* or *) LinearRecurrence[{0, 10, 0, -1}, {1, 1, 5, 9}, 30] (* From Harvey P. Dale, May 06 2012 *)
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CROSSREFS
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Cf. A080871, A080873, A080874, A080875.
Bisections are A001079 and A072256.
Sequence in context: A088974 A105182 A100457 * A173776 A000324 A123817
Adjacent sequences: A080869 A080870 A080871 * A080873 A080874 A080875
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Feb 22 2003
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STATUS
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approved
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