A145718 Numbers x such that there exists n in N with (x+127)^3-x^3=n^2.

762, 1676527, 3403477826, 6909058439031, 14025385227883882, 28471525103545970207, 57797181934813091765106, 117328250856145472737323751, 238176291440793374843675578202, 483497754296559694787188686555087, 981500203045724739624618190031377186

Offset: 1

Author

Richard Choulet, Oct 16 2008

Keywords

• easy
• nonn

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (2031,-2031,1).

Crossrefs

Cf. A145720.

Programs

Magma

I:=[762,1676527]; [n le 2 select I[n] else 2030*Self(n-1)-Self(n-2)+128778: n in [1..20]]; // Vincenzo Librandi, Oct 18 2014

Mathematica

CoefficientList[Series[127 (7 x^2 - 1015 x - 6)/((x - 1) (x^2 - 2030 x + 1)), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 18 2014 *)

PARI

Vec(127*x*(7*x^2-1015*x-6)/((x-1)*(x^2-2030*x+1)) + O(x^20)) \\ Colin Barker, Oct 18 2014

Formula

a(n+2) = 2030*a(n+1)-a(n)+128778.

a(n) = 127*A145720(n). - Colin Barker, Oct 18 2014

G.f.: 127*x*(7*x^2-1015*x-6) / ((x-1)*(x^2-2030*x+1)). - Colin Barker, Oct 18 2014

Extensions

Editing and more terms from Colin Barker, Oct 18 2014