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A145305 Numbers Y such that 237*Y^2+79 is a square. 1
195, 88979085, 40601334443475, 18526470109137550365, 8453665363699081172206755, 3857424412768091666931149169645, 1760150474386452098440318147235146035, 803160181759629441009745959552760456892925, 366483597255522282717242648737403383853920317315 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..180

Index entries for linear recurrences with constant coefficients, signature (456302,-1).

FORMULA

a(n+2) = 456302*a(n+1)-a(n).

a(n) = (195/2)*{[228151+14820*sqrt(237)]^n+[228151-14820*sqrt(237)]^n}-(19/3)*sqrt(237)*{[228151-14820*sqrt(237)]^n-[228151+14820*sqrt(237)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: 195*x*(x+1) / (x^2-456302*x+1). - Colin Barker, Oct 20 2014

EXAMPLE

a(1)=195 because the first relation is : 3002^2=237*195^2+79.

MATHEMATICA

CoefficientList[Series[195 (x + 1)/(x^2 - 456302 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)

LinearRecurrence[{456302, -1}, {195, 88979085}, 20] (* Harvey P. Dale, Jan 19 2020 *)

PROG

(PARI) Vec(195*x*(x+1)/(x^2-456302*x+1) + O(x^20)) \\ Colin Barker, Oct 20 2014

(MAGMA) I:=[195, 88979085]; [n le 2 select I[n] else 456302*Self(n-1)-Self(n-2): n in [1..10]]; // Vincenzo Librandi, Oct 21 2014

CROSSREFS

Sequence in context: A226105 A164130 A084232 * A174890 A077594 A306359

Adjacent sequences:  A145302 A145303 A145304 * A145306 A145307 A145308

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 06 2008

EXTENSIONS

Editing and more terms from Colin Barker, Oct 20 2014

STATUS

approved

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Last modified January 20 10:09 EST 2022. Contains 350471 sequences. (Running on oeis4.)