A008724 a(n) = floor(n^2/12).

0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 21, 24, 27, 30, 33, 36, 40, 44, 48, 52, 56, 60, 65, 70, 75, 80, 85, 90, 96, 102, 108, 114, 120, 126, 133, 140, 147, 154, 161, 168, 176, 184, 192, 200, 208, 216, 225, 234, 243, 252, 261, 270, 280, 290, 300, 310, 320, 330, 341, 352

Offset

0,6

Comments

With a different offset, Molien series for 3-dimensional group [2,n] = *22n.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

P. T. Ho, The crossing number of K_{4,n} on the real projective plane, Discr. Math., 304 (2005), pp. 23-33.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 189.

Eric Weisstein's World of Mathematics, Toroidal Crossing Number.

Index entries for Molien series.

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,1,-2,1).

Formula

a(n) = a(n-6) + n - 3. - Paul Barry, Jul 14 2004

a(n) = Sum_{j=0..n+2} floor(j/6), a(n-2) = (1/2)*floor(n/6)*(2*n - 4 - 6*floor(n/6)). - Mitch Harris, Sep 08 2008

G.f.: x^4/((1-x)^2*(1-x^6)).

Sum_{n>=4} 1/a(n) = Pi^2/18 - Pi/(2*sqrt(3)) + 49/12. - Amiram Eldar, Aug 14 2022

a(n) = a(-n) = A174709(n+2). - Michael Somos, Dec 05 2023

Maple

A008724 := proc(n)
    floor(n^2/12) ;
end proc:
seq(A008724(n), n=0..30) ; # R. J. Mathar, Mar 28 2017

Mathematica

Floor[Range[0, 70]^2/12] (* G. C. Greubel, Sep 09 2019 *)

Prog

(Magma) a008724:=func< n | Floor(n^2/12) >; [ a008724(n): n in [0..70] ];
(PARI) a(n)=n^2\12 \\ Charles R Greathouse IV, Jul 02 2013
(Sage) [floor(n^2/12) for n in (0..70)] # G. C. Greubel, Sep 09 2019
(GAP) List([0..70], n-> Int(n^2/12) ); # G. C. Greubel, Sep 09 2019

Crossrefs

Cf. A001399, A174709.

Sequence in context: A321152 A292983 A174709 * A237118 A112402 A056864

Adjacent sequences: A008721 A008722 A008723 * A008725 A008726 A008727

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Minor edits by Klaus Brockhaus, Nov 24 2010

Status

approved