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A217778
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Expansion of (1-x)^2*(1-3*x)/((1-3*x+x^2)*(1-5*x+5*x^2)).
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4
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1, 3, 10, 34, 117, 407, 1429, 5055, 17986, 64278, 230473, 828391, 2982825, 10754459, 38811802, 140165322, 506449789, 1830590295, 6618524221, 23933966743, 86562282258, 313102489406, 1132598701585, 4097213146599, 14822370816337, 53623952036787
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OFFSET
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0,2
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COMMENTS
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A diagonal of the square array A217770.
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LINKS
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FORMULA
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G.f.: (1-5*x+7*x^2-3*x^3)/(1-8*x+21*x^2-20*x^3+5*x^4).
a(n) = 8*a(n-1) -21*a(n-2) +20*a(n-3) -5*a(n-4) for n>3, a(0)=1, a(1)=3, a(2)=10, a(3)=34.
a(n) = ((3+r)*(5+r)^n-(3-r)*(5-r)^n+(1+r)*(3+r)^n-(1-r)*(3-r)^n)/(4*r*2^n), where r=sqrt(5). [Bruno Berselli, Mar 28 2013]
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MATHEMATICA
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LinearRecurrence[{8, -21, 20, -5}, {1, 3, 10, 34}, 26] (* Bruno Berselli, Mar 28 2013 *)
CoefficientList[Series[(1-x)^2(1-3x)/((1-3x+x^2)(1-5x+5x^2)), {x, 0, 30}], x] (* Harvey P. Dale, Sep 26 2023 *)
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PROG
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(Magma) m:=26; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x)^2*(1-3*x)/((1-3*x+x^2)*(1-5*x+5*x^2)))); // Bruno Berselli, Mar 28 2013
(Maxima) makelist(expand(((3+sqrt(5))*(5+sqrt(5))^n-(3-sqrt(5))*(5-sqrt(5))^n+(1+sqrt(5))*(3+sqrt(5))^n-(1-sqrt(5))*(3-sqrt(5))^n)/(4*2^n*sqrt(5))), n, 0, 25); /* Bruno Berselli, Mar 28 2013 */
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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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