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A201227 a(n) = (A201225(n))^3 - (A201226(n))^2. 2
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^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.
LINKS
FORMULA
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
MATHEMATICA
LinearRecurrence[{19, -19, 1}, {219375, 4566375, 82569375}, 30] (* Harvey P. Dale, Sep 25 2012 *)
CROSSREFS
Sequence in context: A251480 A072189 A187865 * A185531 A258678 A254912
KEYWORD
nonn
AUTHOR
Artur Jasinski, Nov 28 2011
STATUS
approved

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Last modified June 19 03:10 EDT 2024. Contains 373492 sequences. (Running on oeis4.)