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A145716 Numbers Y such that 381*Y^2+127 is a square. 0
13, 26403, 53598077, 108804069907, 220872208313133, 448370474071590083, 910191841493119555357, 1847688989860558625784627, 3750807739225092517223237453, 7614137862937947949404546244963, 15456696110956295112198711654037437 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..11.

Index entries for linear recurrences with constant coefficients, signature (2030,-1).

FORMULA

a(n+2) = 2030*a(n+1)-a(n).

a(n) = (13/2)*{[1015+52*sqrt(381)]^n+[1015-52*sqrt(381)]^n}+(1/3)*sqrt(381)*{[1015+52*sqrt(381)]^n- [1015-52*sqrt(381)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: 13*x*(x+1) / (x^2-2030*x+1). - Colin Barker, Oct 21 2014

EXAMPLE

a(1)=13 because the first relation is 254^2=381*13^2+127.

PROG

(PARI) Vec(13*x*(x+1)/(x^2-2030*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014

CROSSREFS

Sequence in context: A241879 A185408 A123921 * A124990 A013752 A076811

Adjacent sequences:  A145713 A145714 A145715 * A145717 A145718 A145719

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 16 2008

EXTENSIONS

Editing and a(11) from Colin Barker, Oct 21 2014

STATUS

approved

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Last modified January 21 13:47 EST 2020. Contains 331113 sequences. (Running on oeis4.)