A143698 12 times hexagonal numbers: 12*n*(2*n-1).

0, 12, 72, 180, 336, 540, 792, 1092, 1440, 1836, 2280, 2772, 3312, 3900, 4536, 5220, 5952, 6732, 7560, 8436, 9360, 10332, 11352, 12420, 13536, 14700, 15912, 17172, 18480, 19836, 21240, 22692, 24192, 25740, 27336, 28980, 30672, 32412

Offset: 0

Author

Omar E. Pol, Jan 23 2009

Keywords

• easy
• nonn

Comments

Sequence found by reading the line from 0, in the direction 0, 12,..., in the square spiral whose vertices are the generalized tetradecagonal numbers A195818. - Omar E. Pol, Oct 02 2011

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000384, A002939, A085250, A094159, A152746, A154617.

Programs

Maple

seq(12*n*(2*n-1), n=0..40); # G. C. Greubel, May 30 2021

Mathematica

Table[24n^2-12n,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{0,12,72},40] (* Harvey P. Dale, Sep 24 2015 *)

PARI

a(n)=24*n^2-12*n \\ Charles R Greathouse IV, Jun 17 2017

Sage

[12*n*(2*n-1) for n in (0..40)] # G. C. Greubel, May 30 2021

Formula

a(n) = 24*n^2 - 12*n = 12*A000384(n) = 6*A002939(n) = 4*A094159(n) = 3*A085250(n) = 2*A152746(n).

a(n) = a(n-1) + 48*n - 36, with a(0)=0. - Vincenzo Librandi, Dec 14 2010

From G. C. Greubel, May 30 2021: (Start)

G.f.: 12*x*(1 + 3*x)/(1-x)^3.

E.g.f.: 12*x*(1 + 2*x)*exp(x). (End)