A024174 a(n) is floor((4th elementary symmetric function of 1,2,..,n)/(3rd elementary symmetric function of 1,2,...,n)).

0, 0, 1, 2, 3, 4, 6, 8, 10, 13, 16, 19, 22, 25, 29, 33, 37, 42, 47, 52, 57, 62, 68, 74, 80, 87, 94, 101, 108, 115, 123, 131, 139, 148, 157, 166, 175, 184, 194, 204, 214, 225, 236, 247, 258, 269, 281, 293, 305, 318, 331, 344, 357, 370, 384, 398, 412, 427, 442

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Examples

			G.f. = x^5 + 2*x^6 + 3*x^7 + 4*x^8 + 6*x^9 + 8*x^10 + 10*x^11 + 13*x^12 + ...
		

Links

• Ivan Neretin, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A000915, A001303, A011848, A000217.

Programs

Mathematica

Table[Floor[(n - 3) (15 n^3 + 15 n^2 - 10 n - 8)/(120 n (n + 1))], {n, 3, 45}] (* Ivan Neretin, Nov 25 2016 *)
Insert[Table[Floor[1/8 (-2 - 3 n + n^2)], {n, 4, 45}], 0, 1] (* Ralf Steiner, Oct 27 2021 *)

PARI

{a(n) = if( n<4, 0, (n-3) * (15*n^3 + 15*n^2 - 10*n - 8) \ (120 * n * (n+1)))}; /* Michael Somos, Nov 25 2016 */

Formula

Empirical g.f.: x^5*(x^7-2*x^6+2*x^5-2*x^4+x^3-x^2+x-1) / ((x-1)^3*(x^2+1)*(x^4+1)). - Colin Barker, Aug 16 2014

a(n) = floor( A000915(n-3)/A001303(n-2) ). - R. J. Mathar, Sep 23 2016

a(n) = floor((n - 3)*(15n^3 + 15n^2 - 10n - 8)/(120*n*(n + 1))). - Ivan Neretin, Nov 25 2016

a(n) = floor((A000217(n-2)/2 - 1)/2) = floor((n^2 - 3*n - 2)/8), n >= 4. - Ralf Steiner, Oct 25 2021

Extensions

Offset set to 3 by R. J. Mathar, Sep 23 2016