A145121 Numbers n such that there exists x in N : (x+19)^3-x^3=n^2.

361, 108661, 32815261, 9910100161, 2992817433361, 903820954774861, 272950935524574661, 82430278707466772761, 24893671218719440799161, 7517806277774563654573861, 2270352602216699504240506861, 685638968063165475716978498161, 207060698002473756967023265937761

Offset: 1

Author

Richard Choulet, Oct 02 2008

Keywords

• easy
• nonn

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (302,-1).

Programs

Magma

I:=[361,108661]; [n le 2 select I[n] else 302*Self(n-1)-Self(n-2): n in [1..15]]; // Vincenzo Librandi, Oct 19 2014

Mathematica

CoefficientList[Series[361 (1 - x)/(x^2 - 302 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 19 2014 *)

PARI

Vec(-361*x*(x-1)/(x^2-302*x+1) + O(x^20)) \\ Colin Barker, Oct 19 2014

Formula

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

a(n) = 361*A145123(n). - Colin Barker, Oct 19 2014

G.f.: -361*x*(x-1) / (x^2-302*x+1). - Colin Barker, Oct 19 2014

Extensions

Editing and more terms from Colin Barker, Oct 19 2014