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A035328 a(n) = n*(2*n-1)*(2*n+1).

%I A035328 #74 Sep 03 2023 08:42:21
%S A035328 0,3,30,105,252,495,858,1365,2040,2907,3990,5313,6900,8775,10962,
%T A035328 13485,16368,19635,23310,27417,31980,37023,42570,48645,55272,62475,
%U A035328 70278,78705,87780,97527,107970,119133,131040,143715,157182,171465,186588
%N A035328 a(n) = n*(2*n-1)*(2*n+1).
%C A035328 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
%D A035328 Eric Harold Neville, Jacobian Elliptic Functions, 2nd ed., 1951, p. 38.
%D A035328 Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 269
%H A035328 Vincenzo Librandi, <a href="/A035328/b035328.txt">Table of n, a(n) for n = 0..1000</a>
%H A035328 Konrad Knopp, <a href="http://name.umdl.umich.edu/ACM1954.0001.001">Theorie und Anwendung der unendlichen Reihen</a>, Berlin, J. Springer, 1922. (Original German edition of "Theory and Application of Infinite Series")
%F A035328 a(n) = 3*A000447(n) = 3*A000292(2*n-1).
%F A035328 Sum_{n>=1} 1/a(n) = 2*log(2) - 1. - _Benoit Cloitre_, Apr 05 2002
%F A035328 a(n) = A204558(2*n) / (2*n). - _Reinhard Zumkeller_, Jan 18 2012
%F A035328 G.f.: 3*x*(1 + 6*x + x^2)/(1 - x)^4. - _Colin Barker_, Mar 27 2012
%F A035328 Product_{n>=1} 4*n^3/a(n) = Pi/2. - _Daniel Suteu_, Feb 05 2017
%F A035328 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
%F A035328 Sum_{n>=1} (-1)^(n+1)/a(n) = 1 - log(2) (A244009). - _Amiram Eldar_, Jan 30 2021
%F A035328 E.g.f.: exp(x)*x*(3 + 12*x + 4*x^2). - _Stefano Spezia_, Sep 03 2023
%t A035328 Table[n(2n-1)(2n+1),{n,0,40}] (* _Harvey P. Dale_, Jan 11 2014 *)
%o A035328 (Magma)[n*(2*n-1)*(2*n+1): n in [0..40]]; // _Vincenzo Librandi_, Jun 07 2011
%o A035328 (PARI) vector(100,n,(n-1)*(2*n-1)*(2*n-3)) \\ _Derek Orr_, Jan 29 2015
%Y A035328 Cf. A000292, A000447, A027480, A046092, A204558, A244009.
%K A035328 nonn,easy
%O A035328 0,2
%A A035328 _N. J. A. Sloane_
%E A035328 More terms from _Benoit Cloitre_, Apr 05 2002