A133275 Numbers X such that 30*X^2-45 is a square.

3, 63, 1383, 30363, 666603, 14634903, 321301263, 7053992883, 154866542163, 3400009934703, 74645352021303, 1638797734533963, 35978904807725883, 789897108035435463, 17341757471971854303, 380728767275345359203

Offset: 1

Author

Richard Choulet, Oct 16 2007

Keywords

• nonn
• easy

Comments

Positive values of x (or y) satisfying x^2 - 22xy + y^2 + 180 = 0. - Colin Barker, Feb 19 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (22,-1).

Crossrefs

Cf. A157014.

Programs

Magma

I:=[3,63]; [n le 2 select I[n] else 22*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Feb 21 2014

Mathematica

CoefficientList[Series[3 (1 - x)/(1 - 22 x + x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 21 2014 *)

Formula

a(n+2) = 22*a(n+1)-a(n).

a(n+1) = 11*a(n)+2*(30*a(n)^2-45)^0.5.

G.f.: -3*x*(-1+x)/(1-22*x+x^2). - R. J. Mathar, Nov 14 2007

a(n) = 3*A157014(n). - Colin Barker, Feb 19 2014

Extensions

More terms from Paolo P. Lava, Aug 06 2008