A203298 Second elementary symmetric function of the first n terms of (1,2,2,3,3,4,4,5,5...).

2, 8, 23, 47, 91, 151, 246, 366, 540, 750, 1037, 1373, 1813, 2317, 2956, 3676, 4566, 5556, 6755, 8075, 9647, 11363, 13378, 15562, 18096, 20826, 23961, 27321, 31145, 35225, 39832, 44728, 50218, 56032, 62511, 69351, 76931, 84911, 93710, 102950

Offset

2,1

Links

Table of n, a(n) for n=2..41.

Formula

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

Conjectures from Colin Barker, Jan 04 2018: (Start)

a(n) = (6*n^4 + 40*n^3 + 48*n^2 - 112*n) / 192 for n even.

a(n) = (6*n^4 + 40*n^3 + 36*n^2 - 136*n + 54) / 192 for n odd.

a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) for n>9.

(End)

Mathematica

f[k_] := Floor[(k + 2)/2]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 50}]  (* A203298 *)

Crossrefs

Cf. A203246, A203299.

Sequence in context: A158466 A065694 A178129 * A161463 A190021 A014285

Adjacent sequences: A203295 A203296 A203297 * A203299 A203300 A203301

Keyword

nonn

Author

Clark Kimberling, Dec 31 2011

Status

approved