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

Offset

0,5

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).

Formula

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*(-x+x^2+2) / ( (-1+x)^4*(1+x)*(x^2+1) ). - R. J. Mathar, Apr 15 2010

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

Maple

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

Mathematica

CoefficientList[Series[x^4*(-x + x^2 + 2)/((-1 + x)^4*(1 + x)*(x^2 + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Jul 07 2012 *)
Table[(3 ((-1)^n - 1) + 2 (n - 2) (n - 1) n + 6 Sin[(n Pi)/2])/24, {n, 20}] (* Eric W. Weisstein, Jun 20 2017 *)
LinearRecurrence[{3, -3, 1, 1, -3, 3, -1}, {0, 0, 0, 2, 5, 10, 17}, 20] (* Eric W. Weisstein, Jun 20 2017 *)

Prog

(Sage) [floor(binomial(n, 3)/2) for n in range(0, 41)] # [Zerinvary Lajos, Dec 01 2009]
(Magma) [Floor( n*(n-1)*(n-2)/12): n in [0..50]]; // Vincenzo Librandi, Jul 07 2012

Crossrefs

Sequence in context: A172059 A172435 A049688 * A172512 A172982 A178137

Adjacent sequences: A011891 A011892 A011893 * A011895 A011896 A011897

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved