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A145209 Numbers x such that (x+67)^3-x^3 is a square. 1
9782, 10111839727, 10417116202859646, 10731608941013901384311, 11055596214932693950935000742, 11389364664650780372372714547527967, 11733209583865531835599714105766935834286, 12087435181191042877051818694247666912610077671 (list; graph; refs; listen; history; text; internal format)
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+[515095-124*sqrt(17255649))^n}-(2077/1758)*sqrt(17255649)*{[515095-124 *sqrt(17255649)]^n-[515095+124*sqrt(17255649)]^n with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: 67*x*(147*x^2-515095*x-146) / ((x-1)*(x^2-1030190*x+1)). - Colin Barker, Oct 20 2014

EXAMPLE

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

PROG

(PARI) Vec(67*x*(147*x^2-515095*x-146)/((x-1)*(x^2-1030190*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

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Last modified December 8 01:34 EST 2019. Contains 329850 sequences. (Running on oeis4.)