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
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).
Programs
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GAP
List([0..70], n-> Int(n^2/12) ); # G. C. Greubel, Sep 09 2019
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Magma
a008724:=func< n | Floor(n^2/12) >; [ a008724(n): n in [0..70] ];
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Maple
A008724 := proc(n) floor(n^2/12) ; end proc: seq(A008724(n),n=0..30) ; # R. J. Mathar, Mar 28 2017
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Mathematica
Floor[Range[0, 70]^2/12] (* G. C. Greubel, Sep 09 2019 *)
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PARI
a(n)=n^2\12 \\ Charles R Greathouse IV, Jul 02 2013
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Sage
[floor(n^2/12) for n in (0..70)] # G. C. Greubel, Sep 09 2019
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
Extensions
Minor edits by Klaus Brockhaus, Nov 24 2010
Comments