A024403 [ (4th elementary symmetric function of S(n))/(3rd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 2 mod 3}.

1, 3, 5, 9, 13, 18, 24, 30, 37, 45, 54, 64, 74, 85, 97, 109, 122, 136, 151, 167, 183, 200, 218, 236, 255, 275, 296, 318, 340, 363, 387, 411, 436, 462, 489, 517, 545, 574, 604, 634, 665, 697, 730, 764, 798, 833, 869, 905, 942, 980, 1019, 1059, 1099, 1140, 1182, 1224

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A024392, A024393.

Programs

Magma

[(n*(405*n^4+4590*n^3+18495*n^2+30534*n+16376))  div (40*(3*n+10)*(9*(n+1)^2+33*n+55)): n in [1..60]]; // Vincenzo Librandi, Jul 07 2019

Mathematica

Table[Floor[(n (405 n^4 + 4590 n^3 + 18495 n^2 + 30534 n + 16376)) / (40 (3 n + 10) (9 (n+1)^2 + 33 n + 55))], {n, 1, 100}] (* Vincenzo Librandi, Jul 07 2019 *)

Formula

Empirical g.f.: x*(x^2-x+1)*(x^8-x^7-x^5+x^4-x^3-x-1) / ((x-1)^3*(x^2+1)*(x^4+1)). - Colin Barker, Aug 16 2014

a(n) = floor(A024393(n) / A024392(n + 1)). - Sean A. Irvine, Jul 07 2019