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A145721
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Numbers n such that there exists x in N with (x+1)^3-x^3=127*n^2.
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2
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1, 2029, 4118869, 8361302041, 16973439024361, 34456072858150789, 69945810928607077309, 141989961728999508786481, 288239552364058074229479121, 585126149309076161686333829149, 1187805794857872244165183443693349, 2411245178435331346579160704363669321
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OFFSET
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1,2
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (2030,-1).
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FORMULA
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a(n+2) = 2030*a(n+1)-a(n).
a(n) = (1/2)*{[1015+52*sqrt(381)]^n+[1015-52*sqrt(381)]^n}+(13/508)*sqrt(381)*[1015+52*sqrt(381)]^n-[1015-52*sqrt(381)]^n with n>=0. - Paolo P. Lava, Nov 25 2008
a(n) = A145717(n) / 16129. - Colin Barker, Oct 20 2014
G.f.: -x*(x-1) / (x^2-2030*x+1). - Colin Barker, Oct 20 2014
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EXAMPLE
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a(1)=1 because 7^3-6^3=127*1^2.
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MATHEMATICA
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CoefficientList[Series[(1 - x)/(x^2 - 2030 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 20 2014 *)
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PROG
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(PARI) Vec(-x*(x-1)/(x^2-2030*x+1) + O(x^20)) \\ Colin Barker, Oct 20 2014
(MAGMA) I:=[1, 2029]; [n le 2 select I[n] else 2030*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Oct 20 2014
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CROSSREFS
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Cf. A145717.
Sequence in context: A156856 A031543 A031723 * A103126 A045869 A098808
Adjacent sequences: A145718 A145719 A145720 * A145722 A145723 A145724
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KEYWORD
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easy,nonn
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AUTHOR
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Richard Choulet, Oct 16 2008
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EXTENSIONS
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Editing and more terms from Colin Barker, Oct 20 2014
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STATUS
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approved
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