A145307 Numbers x such that there exists n in N : (x+79)^3-x^3=n^2.

7663, 3514673818, 1603752710517223, 731795569310933239378, 333919781866113706302166783, 152368264304339620843780392200938, 69525943738264857888392566815788268343, 31724827179505362919884965402334038047270498

Offset

1,1

Links

Table of n, a(n) for n=1..8.

Index entries for linear recurrences with constant coefficients, signature (456303,-456303,1).

Formula

a(n+2) = 456302*a(n+1)-a(n)+18023850.

G.f.: 79*x*(-97-228151*x+98*x^2) / ( (x-1)*(x^2-456302*x+1) ). - R. J. Mathar, Nov 27 2011

a(n) = 79*A145309(n). - R. J. Mathar, Nov 27 2011

Example

a(1)=7663 because the first relation is : (7663+79)^3-7663^3=118579^2.

Mathematica

LinearRecurrence[{456303, -456303, 1}, {7663, 3514673818, 1603752710517223}, 20] (* Harvey P. Dale, Dec 14 2017 *)

Prog

(PARI) Vec(79*x*(-97-228151*x+98*x^2)/((x-1)*(x^2-456302*x+1)) + O(x^30)) \\ Colin Barker, Oct 18 2014

Crossrefs

Cf. A145306.

Sequence in context: A038011 A205040 A252406 * A232254 A008774 A229508

Adjacent sequences: A145304 A145305 A145306 * A145308 A145309 A145310

Keyword

easy,nonn

Author

Richard Choulet, Oct 06 2008

Extensions

Editing and additional term a(8) from Colin Barker, Oct 18 2014

Status

approved