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A008724 a(n) = floor(n^2/12). 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 (list; graph; refs; listen; history; text; internal format)
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, ToroidalCrossingNumber

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 + 1 (if 1, 2, 3, ... has offset 0). - Paul Barry, Jul 14 2004

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

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

MAPLE

x^4/((1-x)^2*(1-x^6));

MATHEMATICA

s=0; lst={}; Do[AppendTo[lst, s+=n]; AppendTo[lst, s+=n]; AppendTo[lst, s+=n]; AppendTo[lst, s+=n]; AppendTo[lst, s+=n]; AppendTo[lst, s+=n], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 14 2010 *)

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

CROSSREFS

Cf. A001399.

Sequence in context: A120370 A011866 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

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Last modified December 7 11:24 EST 2016. Contains 278874 sequences.