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A102344
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Numbers n such that the Diophantine equation (x+2)^3-x^3=2*n^2 has solutions.
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0
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2, 7, 97, 1351, 18817, 262087, 3650401, 50843527, 708158977, 9863382151, 137379191137, 1913445293767, 26650854921601, 371198523608647, 5170128475599457, 72010600134783751, 1002978273411373057
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| n^2=3*(2*x+4)^2+16
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FORMULA
| a(n+2)=14*a(n+1)-a(n) for n>=2.
G.f.: x(2-21x+x^2)/(1-14x+x^2). a(n)=7*A007655(n+2)-97*A007655(n+1), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 11 2008]
a(n)=-2*sqrt(3)*{[7-4*sqrt(3)]^(n-1)-[7+4*sqrt(3)]^(n-1)}+(7/2)*{[7+4*sqrt(3)]^(n-1)+[7 -4*sqrt(3)]^(n-1)}+[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 25 2008]
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EXAMPLE
| The first examples are 2^3-0^3=2*2^2 ; 5^3-3^3=2*7^2 ; 57^3-55^3=2*97^2 ; 781^3-779^3=2*1351^2 ; 10865^3-10863^3=2*18817^2
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CROSSREFS
| Sequence in context: A076740 A112290 A072059 * A087589 A002812 A192342
Adjacent sequences: A102341 A102342 A102343 * A102345 A102346 A102347
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KEYWORD
| easy,nonn
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AUTHOR
| Richard Choulet (richardchoulet(AT)yahoo.fr), Sep 08 2008
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EXTENSIONS
| Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 11 2008
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