

A014635


a(n) = 2*n*(4*n  1).


20



0, 6, 28, 66, 120, 190, 276, 378, 496, 630, 780, 946, 1128, 1326, 1540, 1770, 2016, 2278, 2556, 2850, 3160, 3486, 3828, 4186, 4560, 4950, 5356, 5778, 6216, 6670, 7140, 7626, 8128, 8646, 9180, 9730, 10296, 10878, 11476, 12090, 12720, 13366, 14028, 14706
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OFFSET

0,2


COMMENTS

Even hexagonal numbers.
Number of edges in the join of two complete graphs of order 3n and n, K_3n * K_n  Roberto E. Martinez II, Jan 07 2002
Bisection of A000384. Also, this sequence arises from reading the line from 0, in the direction 0, 6, ..., in the square spiral whose vertices are the triangular numbers A000217. Perfect numbers are members of this sequence because a(A134708(n)) = A000396(n). Also, positive members are a bisection of A139596.  Omar E. Pol, May 07 2008


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..880
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = C(4*n,2), n>=0.  Zerinvary Lajos, Jan 02 2007
O.g.f.: 2x(3+5x)/(1x)^3.  R. J. Mathar, May 06 2008
a(n) = 8n^2  2n.  Omar E. Pol, May 07 2008
a(n) = a(n1) + 16*n  10 (with a(0)=0).  Vincenzo Librandi, Nov 20 2010
E.g.f.: (8*x^2 + 6*x)*exp(x).  G. C. Greubel, Jul 18 2017
From Vaclav Kotesovec, Aug 18 2018: (Start)
Sum_{n>=1} 1/a(n) = 3*log(2)/2  Pi/4.
Sum_{n>=1} (1)^n / a(n) = log(2)/2 + log(1+sqrt(2))/sqrt(2)  Pi / 2^(3/2). (End)


MAPLE

[seq(binomial(4*n, 2), n=0..43)]; # Zerinvary Lajos, Jan 02 2007


MATHEMATICA

s=0; lst={s}; Do[s+=n++ +6; AppendTo[lst, s], {n, 0, 7!, 16}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)
Table[2*n*(4*n  1), {n, 0, 50}] (* G. C. Greubel, Jul 18 2017 *)


PROG

(MAGMA) [2*n*(4*n1): n in [0..50]]; // Vincenzo Librandi, Apr 25 2011
(PARI) a(n)=2*n*(4*n1) \\ Charles R Greathouse IV, Jun 17 2017


CROSSREFS

Cf. A000217, A000384, A000396, A134708, A139596.
Sequence in context: A081537 A058007 A033588 * A227970 A034955 A117978
Adjacent sequences: A014632 A014633 A014634 * A014636 A014637 A014638


KEYWORD

nonn,easy


AUTHOR

Mohammad K. Azarian


EXTENSIONS

More terms from Erich Friedman


STATUS

approved



