

A145209


Numbers x such that (x+67)^3x^3 is a square.


1



9782, 10111839727, 10417116202859646, 10731608941013901384311, 11055596214932693950935000742, 11389364664650780372372714547527967, 11733209583865531835599714105766935834286, 12087435181191042877051818694247666912610077671
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OFFSET

1,1


LINKS

Colin Barker, Table of n, a(n) for n = 1..166
Index entries for linear recurrences with constant coefficients, signature (1030191,1030191,1).


FORMULA

a(n+2) = 1030190*a(n+1)a(n)+34511298.
a(n) = (67/2)+(19631/4)*{[515095+124*sqrt(17255649)]^n+[515095124*sqrt(17255649))^n}(2077/1758)*sqrt(17255649)*{[515095124 *sqrt(17255649)]^n[515095+124*sqrt(17255649)]^n with n>=0.  Paolo P. Lava, Nov 25 2008
G.f.: 67*x*(147*x^2515095*x146) / ((x1)*(x^21030190*x+1)).  Colin Barker, Oct 20 2014


EXAMPLE

The first relation is : (9782+67)^39782^3=139159^2.


PROG

(PARI) Vec(67*x*(147*x^2515095*x146)/((x1)*(x^21030190*x+1)) + O(x^20)) \\ Colin Barker, Oct 20 2014


CROSSREFS

Sequence in context: A247696 A010092 A023339 * A035911 A069333 A222814
Adjacent sequences: A145206 A145207 A145208 * A145210 A145211 A145212


KEYWORD

easy,nonn


AUTHOR

Richard Choulet, Oct 04 2008, Oct 05 2008


EXTENSIONS

Editing and a(8) from Colin Barker, Oct 20 2014


STATUS

approved



