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A099025
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Expansion of 1 / ((1+x) * (1-5*x+x^2)).
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4
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1, 4, 20, 95, 456, 2184, 10465, 50140, 240236, 1151039, 5514960, 26423760, 126603841, 606595444, 2906373380, 13925271455, 66719983896, 319674648024, 1531653256225, 7338591633100, 35161304909276, 168467932913279, 807178359657120, 3867423865372320
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OFFSET
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0,2
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REFERENCES
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R. C. Alperin, A nonlinear recurrence and its relations to Chebyshev polynomials, Fib. Q., 58:2 (2020), 140-142.
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LINKS
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FORMULA
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G.f.: 1 / ((1 + x) * (1 - 5*x + x^2)).
a(n) = (2^(-n)*(3*(-2)^n+(9-2*sqrt(21))*(5-sqrt(21))^n+(5+sqrt(21))^n*(9+2*sqrt(21))))/21. - Colin Barker, Nov 02 2016
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EXAMPLE
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1 + 4*x + 20*x^2 + 95*x^3 + 456*x^4 + 2184*x^5 + 10465*x^6 + ...
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MATHEMATICA
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CoefficientList[Series[1/((1+x)*(1-5*x+x^2)), {x, 0, 50}], x] (* or *) LinearRecurrence[{4, 4, -1}, {1, 4, 20}, 30] (* G. C. Greubel, Dec 31 2017 *)
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PROG
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(PARI) {a(n) = (3 * (-1)^n + 38 * subst( poltchebi(n), x, 5/2) - 8 * subst( poltchebi(n-1), x, 5/2)) / 21} /* Michael Somos, Jan 25 2013 */
(Magma) I:=[1, 4, 20]; [n le 3 select I[n] else 4*Self(n-1) + 4*Self(n-2) - Self(n-3): n in [1..30]]; // G. C. Greubel, Dec 31 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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