A145717 Numbers n such that there exists x in N with (x+127)^3-x^3=n^2.

16129, 32725741, 66433238101, 134859440619289, 273764598023918569, 555741999129114075781, 1128155984467503549916861, 2290156092727033077217152049, 4649015740079892679247268742609, 9437499662206089411838878330344221, 19158119665262621426140243763330026021

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) = 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