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A035328 a(n) = n*(2*n-1)*(2*n+1). 5
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

Neville, Jacobian Elliptic Functions, 2nd ed., 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

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, A046092.

Sequence in context: A195029 A211617 A180816 * 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 November 12 16:50 EST 2018. Contains 317116 sequences. (Running on oeis4.)