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A247565
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a(n) = 5*a(n-1) - 10*a(n-2) + 8*a(n-3) with a(0) = 2, a(1) = a(2) = 3.
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2
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2, 3, 3, 1, -1, 9, 63, 217, 527, 969, 1311, 1081, 47, -87, 7743, 39961, 121679, 270729, 456543, 548857, 344687, -112791, 380031, 5785561, 24225167, 66310473, 135585183, 208622521, 217744559, 87179049, -72570177, 507315097, 3959709647, 14144835849, 35185603551
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: (2 - 7*x + 8*x^2) / (1 - 5*x + 10*x^2 - 8*x^3).
(n) = a(-1-n) * 2^(2*n+1) for all n in Z.
a(n) = 2^n + A247560(n) for all n in Z.
0 = a(n)*(+4*a(n+1) + 2*a(n+2)) + a(n+1)*(-5*a(n+1) + a(n+2)) for all n in Z.
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EXAMPLE
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G.f. = 2 + 3*x + 3*x^2 + x^3 - x^4 + 9*x^5 + 63*x^6 + 217*x^7 + 527*x^8 + ...
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MATHEMATICA
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CoefficientList[Series[(2-7*x+8*x^2)/(1-5*x+10*x^2-8*x^3), {x, 0, 60}], x] (* or *) LinearRecurrence[{5, -10, 8}, {2, 3, 3}, 60] (* G. C. Greubel, Aug 04 2018 *)
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PROG
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(PARI) {a(n) = 2^n + real( (1 + quadgen(-7))^n )};
(PARI) Vec((2 - 7*x + 8*x^2) / (1 - 5*x + 10*x^2 - 8*x^3) + O(x^50)) \\ Michel Marcus, Sep 22 2014
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((2-7*x+8*x^2)/(1-5*x+10*x^2-8*x^3))); // G. C. Greubel, Aug 04 2018
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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