%I #22 Mar 24 2023 17:42:00
%S 0,1,3,4,6,8,10,13,15,18,22,25,29,33,37,42,46,51,57,62,68,74,80,87,93,
%T 100,108,115,123,131,139,148,156,165,175,184,194,204,214,225,235,246
%N Integer part of ((4th elementary symmetric function of 2,3,...,n+4)/(3rd elementary symmetric function of 2,3,...,n+4)).
%H Ivan Neretin, <a href="/A024182/b024182.txt">Table of n, a(n) for n = 1..10000</a>
%F Empirical g.f.: x^2*(x^6-2*x^5+2*x^4-2*x^3+x^2-1) / ((x-1)^3*(x^2+1)*(x^4+1)). - _Colin Barker_, Aug 16 2014
%F a(n) = floor(1/120 n (15 n^4 + 330 n^3 + 2765 n^2 + 10482 n + 15208)/(n + 6)(n^2 + 11 n + 32)). - _Ivan Neretin_, May 20 2018
%F a(n) = floor(n*(n + 5)/8) for all n in Z. - _Michael Somos_, Mar 23 2023
%e G.f. = x^2 + 3*x^3 + 4*x^4 + 6*x^5 + 8*x^6 + 10*x^7 + ... - _Michael Somos_, Mar 23 2023
%p seq(floor((1/120)*n*(15*n^4+330*n^3+2765*n^2+10482*n+15208)/((n+6)*(n^2+11*n+32))),n=1..50); # _Muniru A Asiru_, May 20 2018
%t Table[Floor[1/120 n (15 n^4 + 330 n^3 + 2765 n^2 + 10482 n + 15208)/(n + 6)/ (n^2 + 11 n + 32)], {n, 42}] (* _Ivan Neretin_, May 20 2018 *)
%t a[ n_] := Quotient[n^2 + 5*n, 8]; (* _Michael Somos_, Mar 23 2023 *)
%o (GAP) List([1..50],n->Int((1/120)*n*(15*n^4+330*n^3+2765*n^2+10482*n+15208)/((n+6)*(n^2+11*n+32)))); # _Muniru A Asiru_, May 20 2018
%o (PARI) {a(n) = (n^2 + 5*n)\8}; /* _Michael Somos_, Mar 23 2023 */
%K nonn
%O 1,3
%A _Clark Kimberling_
%E Missing a(1)=0 added by _Ivan Neretin_, May 20 2018