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A035328
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a(n) = n*(2*n-1)*(2*n+1).
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5
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0, 3, 30, 105, 252, 495, 858, 1365, 2040, 2907, 3990, 5313, 6900, 8775, 10962, 13485, 16368, 19635, 23310, 27417, 31980, 37023, 42570, 48645, 55272, 62475, 70278, 78705, 87780, 97527, 107970, 119133, 131040, 143715, 157182, 171465, 186588
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OFFSET
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0,2
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COMMENTS
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Bisection of A027480. For n>1, gives area of triangle two of whose cevians bound three smaller triangles with areas n-1, n, n+1 contiguously. - Lekraj Beedassy, Dec 21 2006
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REFERENCES
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Neville, Jacobian Elliptic Functions, 2nd ed., p. 38.
Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 269
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original German edition of "Theory and Application of Infinite Series")
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FORMULA
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a(n) = 3*A000447(n) = 3*A000292(2*n-1).
Sum_{n>=1} 1/a(n) = 2*log(2) - 1. - Benoit Cloitre, Apr 05 2002
a(n) = A204558(2*n) / (2*n). - Reinhard Zumkeller, Jan 18 2012
G.f.: 3*x*(1 + 6*x + x^2)/(1 - x)^4. - Colin Barker, Mar 27 2012
Product_{n>=1} 4*n^3/a(n) = Pi/2. - Daniel Suteu, Feb 05 2017
a(n) = Sum_{i=0..2*n} A046092(n-1)+i = Sum_{i=2*n+1..4*n-1} A046092(n-1)+i for n>0. Example: for n = 5, A046092(4) = 40 and a(5) = 40 + 41 + 42 + ... + 49 + 50 = 51 + 52 + 53 + ... + 58 + 59 = 495. - Bruno Berselli, Oct 26 2017
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MATHEMATICA
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Table[n(2n-1)(2n+1), {n, 0, 40}] (* Harvey P. Dale, Jan 11 2014 *)
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PROG
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(MAGMA)[n*(2*n-1)*(2*n+1): n in [0..40]]; // Vincenzo Librandi, Jun 07 2011
(PARI) vector(100, n, (n-1)*(2*n-1)*(2*n-3)) \\ Derek Orr, Jan 29 2015
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CROSSREFS
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Cf. A000292, A000447, A046092.
Sequence in context: A211617 A180816 A308402 * A100259 A031205 A225018
Adjacent sequences: A035325 A035326 A035327 * A035329 A035330 A035331
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Benoit Cloitre, Apr 05 2002
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STATUS
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approved
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