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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A035328 a(n) = n*(2*n-1)*(2*n+1). 6 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 (list; graph; refs; listen; history; text; internal format) OFFSET 0,2 COMMENTS 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 REFERENCES Eric Harold Neville, Jacobian Elliptic Functions, 2nd ed., 1951, p. 38. Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 269 LINKS 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") FORMULA 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 Sum_{n>=1} (-1)^(n+1)/a(n) = 1 - log(2) (A244009). - Amiram Eldar, Jan 30 2021 E.g.f.: exp(x)*x*(3 + 12*x + 4*x^2). - Stefano Spezia, Sep 03 2023 MATHEMATICA Table[n(2n-1)(2n+1), {n, 0, 40}] (* Harvey P. Dale, Jan 11 2014 *) PROG (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 CROSSREFS Cf. A000292, A000447, A027480, A046092, A204558, A244009. Sequence in context: A211617 A180816 A308402 * A100259 A031205 A225018 Adjacent sequences: A035325 A035326 A035327 * A035329 A035330 A035331 KEYWORD nonn,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from Benoit Cloitre, Apr 05 2002 STATUS approved

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Last modified August 18 23:05 EDT 2024. Contains 375284 sequences. (Running on oeis4.)