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 A239364 Numbers n such that (n^2-4)/10 is a square. 2
 38, 1442, 54758, 2079362, 78960998, 2998438562, 113861704358, 4323746327042, 164188498723238, 6234839205156002, 236759701297204838, 8990633810088627842, 341407325082070653158, 12964487719308596192162, 492309126008644584648998, 18694782300609185620469762 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 9 04:17 EDT 2021. Contains 343685 sequences. (Running on oeis4.)