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A106804
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Expansion of g.f.: x*(2 - 9*x - 4*x^2)/((1 - 5*x + x^2)*(1 - 5*x - x^2)).
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1
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0, 2, 11, 56, 285, 1452, 7406, 37816, 193295, 989002, 5065051, 25963276, 133199780, 683904902, 3514119571, 18069536436, 92975574865, 478701242652, 2466137174466, 12711910214796, 65558648361175, 338267429484502
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-25,0,1).
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FORMULA
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G.f.: x*(2 - 9*x - 4*x^2)/((1 - 5*x + x^2)*(1 - 5*x - x^2)).
a(n) = (1/2)*((A052918(n) - 2*A052918(n-1)) - (A004254(n+1) - 6*A004254(n))). - G. C. Greubel, Sep 11 2021
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MATHEMATICA
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M = {{0, 0, 0, 1}, {1, 5, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 5}}; v[1]= {0, 1, 1, 2}; v[n_]:= v[n]= M.v[n-1]; Table[v[n][[1]], {n, 20}]
LinearRecurrence[{10, -25, 0, 1}, {0, 2, 11, 56}, 30] (* Harvey P. Dale, Nov 29 2018 *)
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PROG
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(Magma) I:=[0, 2, 11, 56]; [n le 4 select I[n] else 10*Self(n-1) - 25*Self(n-2) + Self(n-4): n in [1..31]]; // G. C. Greubel, Sep 11 2021
(Sage)
def A106804_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(2-9*x-4*x^2)/((1-5*x+x^2)*(1-5*x-x^2)) ).list()
A106804_list(30) # G. C. Greubel, Sep 11 2021
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CROSSREFS
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Cf. A004254, A052918.
Sequence in context: A212388 A198769 A037554 * A213098 A041129 A332524
Adjacent sequences: A106801 A106802 A106803 * A106805 A106806 A106807
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KEYWORD
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nonn,easy
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AUTHOR
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Roger L. Bagula, May 30 2005
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EXTENSIONS
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Edited by the Associate Editors of the OEIS, Apr 09 2009
Mathematica code fixed by Olivier Gérard, Dec 13 2011
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STATUS
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approved
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