%I #21 Jan 05 2021 19:06:55

%S 38,1442,54758,2079362,78960998,2998438562,113861704358,4323746327042,

%T 164188498723238,6234839205156002,236759701297204838,

%U 8990633810088627842,341407325082070653158,12964487719308596192162,492309126008644584648998,18694782300609185620469762

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

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

%H Colin Barker, <a href="/A239364/b239364.txt">Table of n, a(n) for n = 1..600</a>

%H Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (38,-1).

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

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

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

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

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

%t LinearRecurrence[{38,-1},{38,1442},30] (* _Harvey P. Dale_, Dec 19 2014 *)

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

%Y Cf. A078986, A239365.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Mar 17 2014