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A145721 Numbers n such that there exists x in N with (x+1)^3-x^3=127*n^2. 2
1, 2029, 4118869, 8361302041, 16973439024361, 34456072858150789, 69945810928607077309, 141989961728999508786481, 288239552364058074229479121, 585126149309076161686333829149, 1187805794857872244165183443693349, 2411245178435331346579160704363669321 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (2030,-1).

FORMULA

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

EXAMPLE

a(1)=1 because 7^3-6^3=127*1^2.

MATHEMATICA

CoefficientList[Series[(1 - x)/(x^2 - 2030 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 20 2014 *)

PROG

(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

CROSSREFS

Cf. A145717.

Sequence in context: A156856 A031543 A031723 * A103126 A045869 A098808

Adjacent sequences:  A145718 A145719 A145720 * A145722 A145723 A145724

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 16 2008

EXTENSIONS

Editing and more terms from Colin Barker, Oct 20 2014

STATUS

approved

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Last modified January 20 05:21 EST 2020. Contains 331067 sequences. (Running on oeis4.)