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A097080
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2n^2 - 2n + 3.
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11
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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
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OFFSET
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1,1
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COMMENTS
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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.
This is also the sum of the pairwise averages of five consecutive triangular numnbers in A00217. Start with A000217(0):(0+1)/2 + (1+3)/2 + (3+6)/2 + (6+10)/2 =15, which is the third term of this sequence. Simply continue to create this sequence. - J. M. Bergot, Jun 13 2012
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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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LINKS
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Table of n, a(n) for n=1..49.
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n)=4*(n-1)+a(n-1), (with a(1)=3) [From Vincenzo Librandi, Nov 16 2010]
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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 Joseph Stephan Orlovsky, Mar 01 2009]
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PROG
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(PARI) a(n)=2*n^2-2*n+3 \\ Charles R Greathouse IV, Jun 13 2012
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CROSSREFS
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Cf. A002246, A113136, A113137.
Sequence in context: A213215 A170884 A182836 * A146742 A146425 A147595
Adjacent sequences: A097077 A097078 A097079 * A097081 A097082 A097083
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Nov 02 2008
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STATUS
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approved
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