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Search: id:A001650
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| A001650 |
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n appears n times (n odd). |
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+0
6
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| 1, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For n >= 0, a(n+1) is the number of integers x with |x| <= sqrt(n), or equivalently the number of point in the Z^1 lattice of norm <= n+1. - David W. Wilson, Oct 22 2006
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 106.
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FORMULA
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a(n) = 1 + 2*floor(sqrt(n-1)), n > 0. - Antonio Esposito (antonio.b.esposito(AT)italtel.it), Jan 21 2002
G.f.: theta_3(x)*x/(1-x). a(n+1)=a(n)+A000122(n). - Michael Somos, Apr 29 2003.
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PROGRAM
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(PARI) a(n)=if(n<1, 0, 1+2*sqrtint(n-1))
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CROSSREFS
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Cf. A001670. Partial sums of A000122.
Sequence in context: A136800 A126661 A162226 this_sequence A130175 A101290 A080605
Adjacent sequences: A001647 A001648 A001649 this_sequence A001651 A001652 A001653
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Michael Somos, Apr 29 2003.
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