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A133272
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Indices of centered 7-gonal numbers which are also 7-gonal numbers.
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1, 7, 78, 924, 11005, 131131, 1562562, 18619608, 221872729, 2643853135, 31504364886, 375408525492, 4473397941013, 53305366766659, 635191003258890, 7568986672340016, 90192649064821297, 1074742802105515543
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Numbers X such that 140*X^2-140*X+49 is a square.
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FORMULA
| a(n+2)=12*a(n+1)-a(n)-5 ; a(n+1)=6*a(n)-2.5+0.5*(140*a(n)^2-140*a(n)+49)^0.5
G.f.: x*(-1+6*x)/(-1+x)/(1-12*x+x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
a(n)=(1/2)+(1/4)*[6-sqrt(35)]^(n-1)+(1/20)*sqrt(35)*[6+sqrt(35)]^(n-1)+(1/4)*[6+sqrt(35)]^(n-1)-(1/20)*[6 -sqrt(35)]^(n-1)*sqrt(35), with n>=1 - Paolo P. Lava (paoloplava(AT)gmail.com), Jul 14 2008
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CROSSREFS
| Cf. A128919.
Sequence in context: A107047 A045485 A068621 * A186657 A079590 A202755
Adjacent sequences: A133269 A133270 A133271 * A133273 A133274 A133275
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KEYWORD
| nonn
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AUTHOR
| Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 16 2007
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EXTENSIONS
| More terms from Paolo P. Lava (paoloplava(AT)gmail.com), Jul 14 2008
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