login
A143698
12 times hexagonal numbers: 12*n*(2*n-1).
3
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
0,2
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
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)
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 *)
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jan 23 2009
STATUS
approved