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

1,1

Comments

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

Links

Colin Barker, Table of n, a(n) for n = 1..600

Index entries for linear recurrences with constant coefficients, signature (38,-1).

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).

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A078987, A239364.

Sequence in context: A295413 A202799 A121348 * A277262 A226358 A225796

Adjacent sequences: A239362 A239363 A239364 * A239366 A239367 A239368

Keyword

nonn,easy

Author

Colin Barker, Mar 17 2014

Status

approved