A239365 Numbers n such that 10*n^2+4 is a square.

12, 456, 17316, 657552, 24969660, 948189528, 36006232404, 1367288641824, 51920962156908, 1971629273320680, 74869991424028932, 2843088044839778736, 107962475712487563036, 4099730989029687616632, 155681815107415641868980, 5911809243092764703404608

Offset: 1

Author

Colin Barker, Mar 17 2014

Keywords

• nonn
• easy

Comments

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

Examples

			456 is in the sequence because 10*456^2+4 = 2079364 = 1442^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..600
• Index entries for linear recurrences with constant coefficients, signature (38,-1).

Crossrefs

Cf. A078987, A239364.

Programs

Mathematica

LinearRecurrence[{38,-1},{12,456},20] (* Harvey P. Dale, Aug 04 2022 *)

PARI

Vec(12/(x^2-38*x+1) + O(x^100))

Formula

a(n) = 2*A078987(n-1).

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

G.f.: 12*x / (x^2-38*x+1).