A024178 a(n) = floor((3rd elementary symmetric function of 2,3,...,n+3)/(2+3+...+n+3)).

2, 11, 29, 61, 115, 196, 312, 474, 690, 971, 1331, 1781, 2335, 3010, 3820, 4782, 5916, 7239, 8771, 10535, 12551, 14842, 17434, 20350, 23616, 27261, 31311, 35795, 40745, 46190, 52162, 58696, 65824, 73581, 82005, 91131, 100997, 111644, 123110, 135436

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,-6,5,-5,6,-4,1).

Formula

G.f.: x*(x^3 - 3x^2 + 3x + 2)/((1-x^3)*(1-x)^4).

a(n) = floor((1/24)*n*(n+1)*(n^2 + 9*n + 22)). - Ivan Neretin, May 21 2018

Mathematica

s[n_] := 1 + Range[n + 2]
Table[Floor[SymmetricPolynomial[3, s[n]]/SymmetricPolynomial[1, s[n]]], {n, 1,
  46}] (* Clark Kimberling, Sep 23 2016 *)
LinearRecurrence[{4, -6, 5, -5, 6, -4, 1}, {2, 11, 29, 61, 115, 196, 312}, 40] (* Harvey P. Dale, Dec 05 2018 *)

Crossrefs

Sequence in context: A062123 A345213 A117560 * A009312 A154251 A092275

Adjacent sequences: A024175 A024176 A024177 * A024179 A024180 A024181

Keyword

nonn

Author

Clark Kimberling

Status

approved