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Search: id:A133273
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| A133273 |
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Indices of centered decagonal numbers which are also decagonal numbers. |
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+0
1
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| 1, 10, 171, 3060, 54901, 985150, 17677791, 317215080, 5692193641, 102142270450, 1832868674451, 32889493869660, 590178020979421, 10590314883759910, 190035489886698951, 3410048503076821200, 61190837565496082641
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Numbers X such that 80*X^2-80*X+25 is a square.
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FORMULA
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a(n+2)=18*a(n+1)-a(n)-8 ; a(n+1)=9*a(n)-4+(80*a(n)^2-80*a(n)+25)^0.5
G.f.: x*(-1+9*x)/(-1+x)/(1-18*x+x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
a(n)=(1/2)-(1/8)*sqrt(5)*{[9-4*sqrt(5)]^n-[9+4*sqrt(5)]^n}+(1/4)*{[9-4*sqrt(5)]^n+[9+4*sqrt(5)]^n}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 25 2008]
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CROSSREFS
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Cf. A128922.
Sequence in context: A034830 A098345 A119043 this_sequence A116636 A112703 A132676
Adjacent sequences: A133270 A133271 A133272 this_sequence A133274 A133275 A133276
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KEYWORD
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nonn,new
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AUTHOR
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Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 16 2007
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EXTENSIONS
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More terms from Paolo P. Lava (ppl(AT)spl.at), Nov 25 2008
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