A024172 Integer part of ((3rd elementary symmetric function of 1,2,..,n)/(2nd elementary symmetric function of 1,2,...,n)).

0, 0, 1, 2, 4, 6, 8, 10, 13, 16, 20, 24, 28, 33, 38, 43, 48, 54, 60, 67, 74, 81, 89, 97, 105, 113, 122, 131, 141, 151, 161, 172, 183, 194, 205, 217, 229, 242, 255, 268, 282, 296, 310, 324

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Examples

			a(3) = floor(6/11) = 0; a(4) = floor(50/35) = 1. - _R. J. Mathar_, Sep 15 2009
		

Links

• Ivan Neretin, Table of n, a(n) for n = 2..10000

Programs

GAP

List([2..50],n->Int((1/2)*n*(n-2)*(n+1)/(3*n+2))); # Muniru A Asiru, May 19 2018

Maple

seq(floor((1/2)*n*(n-2)*(n+1)/(3*n+2)),n=2..50); # Muniru A Asiru, May 19 2018

Mathematica

Table[Floor[1/2 (n - 2) n (n + 1)/ (3 n + 2)], {n, 2, 45}] (* Ivan Neretin, May 19 2018 *)

Formula

a(n) = floor( A001303(n-2)/A000914(n-1) ). - R. J. Mathar, Sep 15 2009

Empirical g.f.: x^4*(x^4-x^3+x^2-x+1)*(x^5-x^3-x^2-x-1) / ((x-1)^3*(x^2+x+1)*(x^6+x^3+1)). - Colin Barker, Aug 16 2014

a(n) = floor((1/2)*(n - 2)*n*(n + 1)/(3*n + 2)).

Extensions

Offset set to 2 by R. J. Mathar, Sep 15 2009