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A145717 Numbers n such that there exists x in N with (x+127)^3-x^3=n^2. 2
16129, 32725741, 66433238101, 134859440619289, 273764598023918569, 555741999129114075781, 1128155984467503549916861, 2290156092727033077217152049, 4649015740079892679247268742609, 9437499662206089411838878330344221, 19158119665262621426140243763330026021 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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) = (16129/2)*{[1015+52*sqrt(381)]^n+[1015-52*sqrt(381)]^n}+(1651/4)*sqrt(381)*{[1015+52*sqrt(381)]^n-[1015-52*sqrt(381)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

a(n) = A145721(n)*16129. - Colin Barker, Oct 20 2014

G.f.: -16129*x*(x-1) / (x^2-2030*x+1). - Colin Barker, Oct 20 2014

EXAMPLE

a(1)=16129 because the first relation is (762+127)^3-762^3=16129^2.

MATHEMATICA

CoefficientList[Series[16129 (1 - x)/(x^2 - 2030 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 20 2014 *)

PROG

(PARI) Vec(-16129*x*(x-1)/(x^2-2030*x+1) + O(x^20)) \\ Colin Barker, Oct 20 2014

(MAGMA) I:=[16129, 32725741]; [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. A145721.

Sequence in context: A252603 A335305 A267118 * A184405 A134120 A109566

Adjacent sequences:  A145714 A145715 A145716 * A145718 A145719 A145720

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 November 29 23:37 EST 2020. Contains 338780 sequences. (Running on oeis4.)