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A132593 Nonnegative integer solutions X to the equation: X(X + 1) - 10*Y^2 = 0. 4
0, 9, 360, 13689, 519840, 19740249, 749609640, 28465426089, 1080936581760, 41047124680809, 1558709801289000, 59189925324301209, 2247658452522156960, 85351831270517663289, 3241121929827149048040, 123077281502161146162249 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also, numbers n such that 5*A000217(n) is a square. [Bruno Berselli, Dec 16 2013]

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (39,-39,1).

FORMULA

a(0)=0, a(1)=9 and a(n) = 38*a(n-1) - a(n-2) + 18.

a(n) = -1/2+(1/4)*(19-6*sqrt(10))^n+(1/4)*(19+6*sqrt(10))^n. - Paolo P. Lava, Jul 11 2008

a(n) = (A078986(n) - 1)/2. - Max Alekseyev, Nov 13 2009

G.f.: -9*x*(x+1)/((x-1)*(x^2-38*x+1)). - Colin Barker, Oct 24 2012

MATHEMATICA

LinearRecurrence[{39, -39, 1}, {0, 9, 360}, 30] (* Harvey P. Dale, Jun 01 2014 *)

CROSSREFS

Cf. A007654.

Cf. A233474 (numbers n such that 5*A000217(n)-1 is a square).

Sequence in context: A222697 A063068 A130558 * A162133 A197179 A195888

Adjacent sequences:  A132590 A132591 A132592 * A132594 A132595 A132596

KEYWORD

nonn,easy

AUTHOR

Mohamed Bouhamida, Nov 14 2007

EXTENSIONS

More terms from Max Alekseyev, Nov 13 2009

STATUS

approved

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Last modified April 3 20:29 EDT 2020. Contains 333199 sequences. (Running on oeis4.)