A200335 a(n) = sqrt((A200216(n)+1)/5).

137, 253772063, 472142416783537, 878420022140682133063, 1634298694352222684783778137, 3040609452244043180572708973082863, 5657047804679503550674811676317937783937, 10524926126507566387571141730985597902165021463

Offset: 1

Author

Artur Jasinski, Nov 16 2011

Keywords

• nonn

Comments

All numbers (A200216(n)+1)/5 are perfect squares

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..50
• Index entries for linear recurrences with constant coefficients, signature (1860497, 1860497, -1).

Crossrefs

Cf. A200216, A200217, A200218.

Programs

Magma

I:=[137, 253772063, 472142416783537]; [n le 3 select I[n] else 1860497*Self(n-1)+1860497*Self(n-2)-Self(n-3): n in [1..30]]; // Vincenzo Librandi, Nov 18 2011

Mathematica

aa = {}; uu = 682 + 61*Sqrt[125]; Do[vv = Expand[uu^(2*n - 1)]; tt = ((-1)^n vv[[1]] + 57)/125; xx = (5^5*tt^2 - 3000*tt + 719); yy = Round[N[Sqrt[xx^3], 1000]]; dd = xx^3 - yy^2; AppendTo[aa, Sqrt[(xx + 1)/5]], {n, 1, 20}]; aa

PARI

x='x+O('x^30); Vec((137 -1116026*x +137*x^2)/(1 - 1860497*x - 1860497*x^2 + x^3)) \\ G. C. Greubel, Jul 10 2018

Formula

G.f.: (137 - 1116026*x + 137*x^2)/(1 - 1860497*x - 1860497*x^2 + x^3).

a(n) = 1860497*a(n-1) + 1860497*a(n-2) - a(n-3). [corrected by Vincenzo Librandi, Nov 18 2011]