



219375, 4566375, 82569375, 1482276375, 26598999375, 477300306375, 8564807109375, 153689228256375, 2757841302099375, 49487454210126375, 888016334480769375, 15934806566444316375, 285938501861517519375, 5130958226940871626375, 92071309583074172349375
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Values d of solutions (x,y,d) of x^3y^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.


LINKS



FORMULA

a(n) = 19*a(n1)  19*a(n2) + a(n3).
G.f.: x*(3375*(65118*x+7*x^2))/((1+x)*(118*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


MATHEMATICA

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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



