A201226 -id:A201226 - cp's OEIS frontend

A201227 a(n) = (A201225(n))^3 - (A201226(n))^2.

219375, 4566375, 82569375, 1482276375, 26598999375, 477300306375, 8564807109375, 153689228256375, 2757841302099375, 49487454210126375, 888016334480769375, 15934806566444316375, 285938501861517519375, 5130958226940871626375, 92071309583074172349375

Offset: 1

Artur Jasinski, Nov 28 2011

nonn

Values d of solutions (x,y,d) of x^3-y^2 = d with decreasing coefficient r=sqrt(x)/d which r tend to 1/(1350*sqrt(5)) when d tends to infinity.
Also infinity family of solutions Mordell curve with extension sqrt(5) (another than A200218).
Conjecture: No more infinite families of solutions Mordell curves with extension sqrt(5) than A201227 and A200218.
Ratio a(n+1)/a(n) tends to 9+4*sqrt(5) when n tends to infinity.
Because all values in this sequence are positive, it means that A201225, A201226 and A201227 are even indexes subset of another sequence.

Index entries for linear recurrences with constant coefficients, signature (19, -19, 1).

LinearRecurrence[{19,-19,1},{219375,4566375,82569375},30] (* Harvey P. Dale, Sep 25 2012 *)

a(n) = (A201225(n))^3 - (A201226(n))^2.
a(n) = 19*a(n-1) - 19*a(n-2) + a(n-3).
G.f.: x*(3375*(-65-118*x+7*x^2))/((-1+x)*(1-18*x+x^2)).
a(n) = 3375*(-11-(-2+sqrt(5))*(9+4*sqrt(5))^(-n)+(2+sqrt(5))*(9+4*sqrt(5))^n). - Colin Barker, Mar 03 2016

cp's OEIS Frontend

A201227 a(n) = (A201225(n))^3 - (A201226(n))^2.

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