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A105073
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Define a(1)=0, a(2)=2 then a(n)=3*a(n-1)-a(n-2), a(n+1)=3*a(n)-a(n-1) and a(n+2)=3*a(n+1)-a(n)+2 This sequence is such that 20*(a(n)^2)+20*a(n)+1 = j^2 = a square.
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0
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0, 2, 6, 16, 44, 116, 304, 798, 2090, 5472, 14328, 37512, 98208, 257114, 673134, 1762288, 4613732, 12078908, 31622992, 82790070, 216747218, 567451584, 1485607536, 3889371024, 10182505536, 26658145586, 69791931222, 182717648080
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| (1/6) [Fib(2n+4) - 2*Fib(2n) - 2*cos((n+2)(2Pi/3)) - 4 ]. - Ralf Stephan, May 20 2007
a(n)= 3*a(n-1) -a(n-2) +a(n-3) -3*a(n-4) +a(n-5). G.f.: 2*x^2/((1-x) * (1+x+x^2) * (1-3*x+x^2)). a(n) = A061347(n+2)/6+A001519(n+2)/2-2/3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 13 2009]
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CROSSREFS
| Sequence in context: A027068 A003142 A118041 * A002605 A026134 A105696
Adjacent sequences: A105070 A105071 A105072 * A105074 A105075 A105076
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KEYWORD
| nonn
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AUTHOR
| Pierre CAMI (pierre-cami(AT)bbox.fr), Apr 06 2005
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EXTENSIONS
| Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 13 2009
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