A239364 Numbers n such that (n^2-4)/10 is a square.

38, 1442, 54758, 2079362, 78960998, 2998438562, 113861704358, 4323746327042, 164188498723238, 6234839205156002, 236759701297204838, 8990633810088627842, 341407325082070653158, 12964487719308596192162, 492309126008644584648998, 18694782300609185620469762

Offset: 1

Author

Colin Barker, Mar 17 2014

Keywords

• nonn
• easy

Comments

Values of x satisfying the Pellian equation x^2 - 10*y^2 = 4.

Examples

			1442 is in the sequence because (1442^2-4)/10 = 207936 = 456^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..600
• Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
• Index entries for linear recurrences with constant coefficients, signature (38,-1).

Crossrefs

Cf. A078986, A239365.

Programs

Mathematica

LinearRecurrence[{38,-1},{38,1442},30] (* Harvey P. Dale, Dec 19 2014 *)

PARI

Vec(-2*x*(x-19)/(x^2-38*x+1) + O(x^100))

Formula

a(n) = 2*A078986(n).

a(n) = (19+6*sqrt(10))^(-n)+(19+6*sqrt(10))^n.

a(n) = 38*a(n-1)-a(n-2).

G.f.: -2*x*(x-19) / (x^2-38*x+1).