A024202 a(n) = [ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 odd positive integers}.

1, 11, 38, 96, 205, 385, 662, 1068, 1635, 2401, 3410, 4706, 6339, 8365, 10840, 13826, 17391, 21603, 26536, 32270, 38885, 46467, 55108, 64900, 75941, 88335, 102186, 117604, 134705, 153605, 174426, 197296, 222343, 249701, 279510, 311910, 347047, 385073

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A024197.

Programs

Maple

f:= proc(n)
  if n mod 3 = 1 then (n^4+4*n^3+4*n^2+n-4)/6
  else n*(n+1)*(n^2+3*n+1)/6
  fi
end proc:
map(f, [$1..100]); # Robert Israel, Dec 30 2016

Mathematica

Table[Floor[n*(n + 1)*(n^2 + 3*n + 1)/6], {n, 1, 50}] (* G. C. Greubel, Dec 30 2016 *)

PARI

for(n=1,25, print1(floor(n*(n+1)*(n^2+3*n+1)/6), ", ")) \\ G. C. Greubel, Dec 30 2016

Formula

Empirical g.f.: x*(x^4-5*x^3-7*x-1) / ((x-1)^5*(x^2+x+1)). - Colin Barker, Aug 15 2014

From Robert Israel, Dec 30 2016: (Start)

a(n) = floor(A024197(n)/(n+2)^2) = floor(n*(n+1)*(n^2+3*n+1)/6).

a(n) = (n^4+4*n^3+4*n^2+n-4)/6 if n == 1 (mod 3).

Otherwise a(n) = n*(n+1)*(n^2+3*n+1)/6.

The empirical g.f. can be obtained from this. (End)