0,2

a(n)/A159993(n) approximates the positive root of x^3+2*x^2+10*x=20:

A159994(n)/A159995(n) = f(a(n)/A159993(n)) --> 0,

where f(x) = x^3 + 2*x^2 + 10*x - 20;

a(n)/A159993(n)=a(n-1)/A159993(n-1))+A159990(n)/A159991(n).

R. Zumkeller, Table of n, a(n) for n = 0..30

a(0)/A159993(0) = 1;

a(1)/A159993(1) = 41/30;

a(2)/A159993(2) = 4927/3600;

a(3)/A159993(3) = 49277/36000;

a(4)/A159993(4) = 5913251/4320000;

a(5)/A159993(5) = 33262037/24300000;

a(6)/A159993(6) = 31931555539/23328000000;

a(7)/A159993(7) = 127726222157/93312000000;

a(8)/A159993(8) = 4598143997653/3359232000000;

and written as decimal fractions:

a(0)/A159993(0) = 1;

a(1)/A159993(1) ~= 1.3666666666666667;

a(2)/A159993(2) ~= 1.3686111111111111;

a(3)/A159993(3) ~= 1.3688055555555556;

a(4)/A159993(4) ~= 1.3688081018518519;

a(5)/A159993(5) ~= 1.3688081069958847;

a(6)/A159993(6) ~= 1.3688081078103566;

a(7)/A159993(7) ~= 1.3688081078210733;

a(8)/A159993(8) ~= 1.3688081078213710.

Sequence in context: A107690 A068815 A093174 this_sequence A101830 A091758 A104301

Adjacent sequences: A159989 A159990 A159991 this_sequence A159993 A159994 A159995

frac,nonn

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 01 2009