A145124 Numbers x such that there exists n in N : (x+1)^3-x^3=19*n^2.

2, 757, 228762, 69085517, 20863597522, 6300737366277, 1902801821018282, 574639849210155037, 173539331659645803042, 52408303521363822363797, 15827134124120214708063802, 4779742097180783478012904557, 1443466286214472490145189112562

Offset

1,1

Links

Table of n, a(n) for n=1..13.

Index entries for linear recurrences with constant coefficients, signature (303,-303,1).

Formula

a(n+2) = 302*a(n+1)-a(n)+150.

G.f.: x*(-2-151*x+3*x^2) / ( (x-1)*(x^2-302*x+1) ). - R. J. Mathar, Nov 27 2011

Example

a(1)=2 because 3^3-2^3=19*1.

Mathematica

CoefficientList[Series[(-2 - 151*x + 3*x^2)/((x - 1)*(x^2 - 302*x + 1)), {x, 0, 15}], x] (* Wesley Ivan Hurt, Sep 04 2022 *)

Prog

(PARI) Vec(x*(-2-151*x+3*x^2)/((x-1)*(x^2-302*x+1)) + O(x^30)) \\ Colin Barker, Oct 18 2014

Crossrefs

Cf. A145123.

Sequence in context: A151591 A252986 A247080 * A102969 A179960 A344663

Adjacent sequences: A145121 A145122 A145123 * A145125 A145126 A145127

Keyword

easy,nonn

Author

Richard Choulet, Oct 02 2008

Extensions

Editing and more terms from Colin Barker, Oct 18 2014

Status

approved