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
Keywords
Links
- Ivan Neretin, Table of n, a(n) for n = 1..10000
Programs
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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 *)
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((1/2)*n*(5+n)*(n^2 + 9*n + 22)/(3*n^2 + 29*n + 72)). - Ivan Neretin, May 21 2018
Extensions
Definition corrected by R. J. Mathar, Sep 23 2016