A145720 Numbers x such that there exists n in N with (x+1)^3-x^3=127*n^2.

6, 13201, 26799038, 54402034953, 110436104156566, 224185237035795041, 455095920746559777678, 923844494930279312892313, 1875403869612546258611618726, 3807068931468973974702273122481, 7728348055478147556099355827018718, 15688542745551708069907717626574876073

Offset: 1

Author

Richard Choulet, Oct 16 2008

Keywords

• easy
• nonn

Examples

			a(1)=6 because the first relation is 7^3-6^3=127*1^2.
		

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. A145718.

Programs

Magma

I:=[6,13201]; [n le 2 select I[n] else 2030*Self(n-1)-Self(n-2)+1014: n in [1..20]]; // Vincenzo Librandi, Oct 18 2014

Mathematica

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

PARI

Vec(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)+1014.

a(n) = A145718(n)/127. - Colin Barker, Oct 18 2014

G.f.: 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