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Search: id:A103715
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| A103715 |
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Define a(1)=0, a(2)=0, a(3)=1, a(4)=3, a(5)=18, a(6)=22, a(7)=119, a(8)=285 such that from i=1 to 8 : 420*(a(i)^2)+420*a(i)+1=j(i)^2, j(1)=1, j(2)=1, j(3)=29, j(4)=71, j(5)=379, j(6)=461, j(7)=2449, j(8)=5841 Then a(n)=a(n-8)+4*sqrt(420*(a(n-4)^2)+420*a(n-4)+1). |
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| 0, 0, 1, 3, 18, 22, 119, 285, 1516, 1844, 9797, 23407, 124334, 151226, 803275, 1919129, 10193912, 12398728, 65858793, 157345211, 835776490, 1016544510, 5399617791, 12900388213, 68523478308, 83344251132, 442702800109
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OFFSET
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1,4
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COMMENT
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By construction a(n) is integer so 420*((a(n)^2)+420*a(n)+1=j(n)^2
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FORMULA
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a(n) = a(n-1) +82*a(n-4) -82*a(n-5) -a(n-8) +a(n-9). G.f.: x^3*(x^2+1)*(x^4+2*x^3+14*x^2+2*x+1)/((1-x)*(x^8-82*x^4+1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 13 2009]
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CROSSREFS
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Cf. A103200, A053141.
Sequence in context: A098874 A077104 A073815 this_sequence A131860 A048080 A118474
Adjacent sequences: A103712 A103713 A103714 this_sequence A103716 A103717 A103718
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KEYWORD
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nonn
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AUTHOR
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Pierre CAMI (pierrecami(AT)tele2.fr), Mar 27 2005
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EXTENSIONS
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Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 13 2009
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