OFFSET
1,1
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).
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]
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
PROG
(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
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Nov 16 2011
STATUS
approved