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A084070
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a(0)=0, a(1)=6, a(n)=38*a(n-1)-a(n-2).
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2
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0, 6, 228, 8658, 328776, 12484830, 474094764, 18003116202, 683644320912, 25960481078454, 985814636660340, 37434995712014466, 1421544022419889368, 53981237856243781518, 2049865494514843808316, 77840907553707820934490, 2955904621546382351702304
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) solves for y in the Diophantine equation x^2-10*y^2=1, The corresponding x solutions are provided by A078986. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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LINKS
| Tanya Khovanova, Recursive Sequences
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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 (mathar(AT)strw.leidenuniv.nl), 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 (paoloplava(AT)gmail.com), Jul 11 2008
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MATHEMATICA
| LinearRecurrence[{38, -1}, {0, 6}, 30] (* From Harvey P. Dale, Nov 01 2011 *)
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PROG
| (PARI) u=0; v=6; for(n=2, 20, w=38*v-u; u=v; v=w; print1(w, ", "))
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CROSSREFS
| Cf. A001653, A001353, A060645, A001078, A001109, A084068, A084069.
Cf. A078986 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Apr 14 2010]
Sequence in context: A130644 A166502 A173083 * A177043 A117064 A112001
Adjacent sequences: A084067 A084068 A084069 * A084071 A084072 A084073
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), May 10 2003
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