A011894 a(n) = floor(n*(n-1)*(n-2)/12).

0, 0, 0, 0, 2, 5, 10, 17, 28, 42, 60, 82, 110, 143, 182, 227, 280, 340, 408, 484, 570, 665, 770, 885, 1012, 1150, 1300, 1462, 1638, 1827, 2030, 2247, 2480, 2728, 2992, 3272, 3570, 3885, 4218, 4569, 4940, 5330, 5740, 6170, 6622, 7095, 7590, 8107, 8648, 9212, 9800

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n+1) = floor((n^3-n)/12) is an upper bound for the Kirchhoff index of a circulant graph with n vertices [Zhang & Yang]. - R. J. Mathar, Apr 26 2007

Also the matching number of the n-tetrahedral graph. - Eric W. Weisstein, Jun 20 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Johnson Graph
• Eric Weisstein's World of Mathematics, Matching Number
• Eric Weisstein's World of Mathematics, Tetrahedral Graph
• H. Zhang and Y. Yang, Resistance Distance and Kirchhoff Index in Circulant Graphs, Int. J. Quant. Chem. 107 (2007) 330-339.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1,-3,3,-1).

Crossrefs

Cf. A011886.

Programs

Magma

[Floor(n*(n-1)*(n-2)/12): n in [0..50]]; // Vincenzo Librandi, Jul 07 2012

Maple

seq(floor(binomial(n,3)/2), n=0..40); # Zerinvary Lajos, Jan 12 2009

Mathematica

CoefficientList[Series[x^4*(2-x+x^2)/((1-x)^3*(1-x^4)),{x, 0, 50}], x] (* Vincenzo Librandi, Jul 07 2012 *)
(* Contributions from Eric W. Weisstein, Jun 20 2017 *)
Table[(3*((-1)^n -1) + 2*n*(n-1)*(n-2) + 6*Sin[(n*Pi)/2])/24, {n,0,50}]
LinearRecurrence[{3,-3,1,1,-3,3,-1}, {0,0,0,2,5,10,17}, 50] (* End *)
Floor[Binomial[Range[0,50], 3]/2] (* G. C. Greubel, Oct 06 2024 *)

Sage

[floor(binomial(n,3)/2) for n in range(41)] # Zerinvary Lajos, Dec 01 2009

Formula

From R. J. Mathar, Apr 15 2010: (Start)

a(n) = +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7).

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

a(n) = (1/24)*(2*n^3 - 6*n^2 + 4*n - 3*(1-(-1)^n)*(1 - (-1)^((2*n-1+(-1)^n)/4)) ). - Luce ETIENNE, Jun 26 2014