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A084070 a(0)=0, a(1)=6, a(n)=38*a(n-1)-a(n-2). 5
0, 6, 228, 8658, 328776, 12484830, 474094764, 18003116202, 683644320912, 25960481078454, 985814636660340, 37434995712014466, 1421544022419889368, 53981237856243781518, 2049865494514843808316, 77840907553707820934490, 2955904621546382351702304 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This sequence gives the values of y in solutions of the Diophantine equation x^2 - 10*y^2 = 1. The corresponding x values are in A078986. - Vincenzo Librandi, Aug 08 2010 [edited by Jon E. Schoenfield, May 04 2014]

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..632

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (38, -1).

FORMULA

Numbers n such that 10*n^2=floor(n*sqrt(10)*ceil(n*sqrt(10))).

a(n) = 37*(a(n-1)+a(n-2))-a(n-3). a(n) = 39*(a(n-1)-a(n-2))+a(n-3). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 20 2006

O.g.f.: 6*x/(1-38*x+x^2). a(n) = 6*A078987(n-1). - R. J. Mathar, Feb 19 2008

a(n)=(1/20)*[19+6*sqrt(10)]^n*sqrt(10)-(1/20)*[19-6*sqrt(10)]^n*sqrt(10), with n>=0. - Paolo P. Lava, Jul 11 2008

MATHEMATICA

LinearRecurrence[{38, -1}, {0, 6}, 30] (* Harvey P. Dale, Nov 01 2011 *)

PROG

(PARI) u=0; v=6; for(n=2, 20, w=38*v-u; u=v; v=w; print1(w, ", "))

CROSSREFS

Cf. A001653, A001353, A060645, A001078, A001109, A084068, A084069, A221874.

Cf. A078986. - Vincenzo Librandi, Apr 14 2010

Sequence in context: A233142 A166502 A173083 * A282736 A277293 A177043

Adjacent sequences:  A084067 A084068 A084069 * A084071 A084072 A084073

KEYWORD

nonn

AUTHOR

Benoit Cloitre, May 10 2003

STATUS

approved

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Last modified May 28 19:46 EDT 2017. Contains 287241 sequences.