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

3,4

Links

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

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

Example

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 + ...

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 *)

Prog

(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 */

Crossrefs

Cf. A000915, A001303, A011848, A000217.

Sequence in context: A100919 A184109 A214780 * A008739 A280706 A025695

Adjacent sequences: A024171 A024172 A024173 * A024175 A024176 A024177

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved