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Search: id:A072329
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| A072329 |
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a(n+1)=3*a(n-2)+2*a(n-1) a(n)=x^n+y^n+z^n. |
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+0
1
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| 3, 0, 4, 9, 8, 30, 43, 84, 176, 297, 604, 1122, 2099, 4056, 7564, 14409, 27296, 51510, 97819, 184908, 350168, 663273, 1255060, 2377050
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OFFSET
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0,1
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COMMENT
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With the terms indexed as shown, has property that n prime or n=2^k or n=3^k => n divides a(n).
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FORMULA
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a(n)=x^n+y^n+z^n e=-1/2+i*sqrt(3)/2, e^2=-1/2-i*sqrt(3)/2 x=((3+sqrt(9-32/27)/2)^(1/3)+((3-sqrt(9-32/27))/2)^(1/3) y=e*((3+sqrt(9-32/27))/2)^(1/3)+(e^2)*((3-sqrt(9-32/27))/2)^(1/3) z=(e^2)*((3+sqrt(9-32/27)/2)^(1/3)+e*((3-sqrt(9-32/27))/2)^(1/3)
G.f.: g(x)=(3-2*x^2)/(1-2*x^2-3*x^3)
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CROSSREFS
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Cf. A001608.
Sequence in context: A021332 A008344 A088230 this_sequence A068630 A079406 A068627
Adjacent sequences: A072326 A072327 A072328 this_sequence A072330 A072331 A072332
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KEYWORD
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easy,nonn
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AUTHOR
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M. Kristof (kristmikl(AT)freemail.hu), Jul 15 2002
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
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