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Search: id:A097080
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| A097080 |
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a(n) = 2*n^2 - 2*n + 3. |
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+0
5
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| 3, 7, 15, 27, 43, 63, 87, 115, 147, 183, 223, 267, 315, 367, 423, 483, 547, 615, 687, 763, 843, 927, 1015, 1107, 1203, 1303, 1407, 1515, 1627, 1743, 1863, 1987, 2115, 2247, 2383, 2523, 2667, 2815, 2967, 3123, 3283, 3447, 3615, 3787, 3963, 4143, 4327, 4515, 4707
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The rational numbers may be totally ordered, first by height (see A002246) and then by magnitude; every rational number of height n appears in this ordering at a position <= a(n).
This ordering of the rationals is given in A113136/A113137.
The old entry with this sequence number was a duplicate of A027356.
Except for the first term, a(n)=4*n+a(n-1), (with a(1)=7) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
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REFERENCES
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M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 7.
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FORMULA
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Except for the first term, a(n)=4*n+a(n-1), (with a(1)=7) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
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EXAMPLE
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For n=2, a(2)=4*2+7=15; n=3, a(3)=4*3+15=27; n=4, a(4)=4*4+27=43 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
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MATHEMATICA
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a=3; lst={}; Do[a+=n; AppendTo[lst, a], {n, 0, 6!, 4}]; lst...and/or... lst={}; Do[AppendTo[lst, 2*n^2-2*n+3], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 01 2009]
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CROSSREFS
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Cf. A002246, A113136, A113137.
Sequence in context: A051054 A001649 A001276 this_sequence A146742 A146425 A147595
Adjacent sequences: A097077 A097078 A097079 this_sequence A097081 A097082 A097083
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 02 2008
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