A024180 a(n) = floor((3rd elementary symmetric function of 2,3,...,n+3) / (2nd elementary symmetric function of 2,3,...,n+3) ).

0, 2, 3, 5, 7, 10, 13, 16, 20, 24, 28, 32, 37, 42, 48, 54, 60, 67, 74, 81, 88, 96, 104, 113, 122, 131, 141, 151, 161, 171, 182, 193, 205, 217, 229, 242, 255, 268, 281, 295, 309, 324, 339, 354, 370, 386, 402, 418, 435, 452, 470, 488

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

Empirical g.f.: -x^2*(x^10-2*x^9+x^7+x^4+x^2-x+2) / ((x-1)^3*(x^2+x+1)*(x^6+x^3+1)). - Colin Barker, Aug 16 2014

a(n) = floor(A001702(n+1)/A001701(n+2)). - R. J. Mathar, Sep 23 2016

a(n) = floor((1/2)*n*(5+n)*(n^2 + 9*n + 22)/(3*n^2 + 29*n + 72)). - Ivan Neretin, May 21 2018

Mathematica

s[n_] := 1 + Range[n + 2]
Table[Floor[SymmetricPolynomial[3, s[n]]/SymmetricPolynomial[2, s[n]]], {n, 1,
  46}] (* Clark Kimberling, Sep 23 2016 *)

Crossrefs

Sequence in context: A101433 A225645 A302334 * A183137 A008738 A022790

Adjacent sequences: A024177 A024178 A024179 * A024181 A024182 A024183

Keyword

nonn

Author

Clark Kimberling

Extensions

Definition corrected by R. J. Mathar, Sep 23 2016

Status

approved