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

1,1

Comments

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

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).

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).

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A078986, A239365.

Sequence in context: A170757 A218740 A158702 * A078987 A009982 A041685

Adjacent sequences: A239361 A239362 A239363 * A239365 A239366 A239367

Keyword

nonn,easy

Author

Colin Barker, Mar 17 2014

Status

approved