A145122 Numbers X such that (X+19)^3-X^3 is a square

38, 14383, 4346478, 1312624823, 396408352918, 119714009959263, 36153234599347358, 10918157134992945703, 3297247301533270257798, 995757766905912624912143, 300715548358284079453212238

Offset

1,1

Links

Table of n, a(n) for n=1..11.

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

Formula

a(n+2)=302*a(n+1)-a(n)+2850

a(n)=19*A145124(n). G.f.: 19*x*(-2-151*x+3*x^2)/((x-1)*(x^2-302*x+1)). - R. J. Mathar, Oct 26 2009.

Example

a(1)=38 because 57^3-38^3=361^2

Mathematica

LinearRecurrence[{303, -303, 1}, {38, 14383, 4346478}, 20] (* Harvey P. Dale, Sep 24 2016 *)

Crossrefs

Sequence in context: A145120 A183581 A030260 * A134182 A110017 A181016

Adjacent sequences: A145119 A145120 A145121 * A145123 A145124 A145125

Keyword

easy,nonn

Author

Richard Choulet, Oct 02 2008

Status

approved