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A117691
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Expansion of -(x^7+x^6+x^5-2*x^3-3*x^2-3*x-4) / ((x-1)^2*(x+1)^2*(x^2+1)^2).
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0
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4, 3, 3, 2, 8, 5, 5, 3, 12, 7, 7, 4, 16, 9, 9, 5, 20, 11, 11, 6, 24, 13, 13, 7, 28, 15, 15, 8, 32, 17, 17, 9, 36, 19, 19, 10, 40, 21, 21, 11, 44, 23, 23, 12, 48, 25, 25, 13, 52, 27, 27, 14, 56, 29, 29, 15, 60, 31, 31, 16, 64, 33, 33, 17, 68, 35, 35, 18, 72, 37, 37, 19, 76, 39, 39, 20
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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..75.
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FORMULA
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G.f.: -(x^7+x^6+x^5-2*x^3-3*x^2-3*x-4) / ((x-1)^2*(x+1)^2*(x^2+1)^2). - Colin Barker, Mar 15 2013
a(n) = 2*a(n-4) - a(n-8). - Colin Barker, Mar 15 2013
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MATHEMATICA
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o = Table[Abs[Coefficient[ExpandAll[(x - (a + I*Sqrt[2*a + 1])/(a + 1))*(x - ( a - I*Sqrt[2*a + 1])/(a + 1))], x]], {a, 1, 100}]; rational = Table[{Numerator[o[[n]]], Denominator[o[[n]]]}, {n, 2, 100}]; Flatten[rational]
t = {4, 3, 3, 2, 8, 5, 5, 3}; Do[AppendTo[t, 2*t[[-4]] - t[[-8]]], {100}]; t (* T. D. Noe, Mar 17 2013 *)
LinearRecurrence[{0, 0, 0, 2, 0, 0, 0, -1}, {4, 3, 3, 2, 8, 5, 5, 3}, 80] (* Harvey P. Dale, Jan 30 2021 *)
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CROSSREFS
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Sequence in context: A117323 A016502 A305743 * A243564 A358329 A171627
Adjacent sequences: A117688 A117689 A117690 * A117692 A117693 A117694
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KEYWORD
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nonn,easy
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AUTHOR
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Roger L. Bagula, Apr 12 2006
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EXTENSIONS
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New name from Colin Barker, Mar 17 2013
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STATUS
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approved
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