A203246 Second elementary symmetric function of the first n terms of (1,1,2,2,3,3,4,4,...).

1, 5, 13, 31, 58, 106, 170, 270, 395, 575, 791, 1085, 1428, 1876, 2388, 3036, 3765, 4665, 5665, 6875, 8206, 9790, 11518, 13546, 15743, 18291, 21035, 24185, 27560, 31400, 35496, 40120, 45033, 50541, 56373, 62871, 69730, 77330, 85330, 94150

Offset

2,2

Comments

Second subdiagonal of A246117. - Peter Bala, Aug 15 2014

Links

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

Formula

Conjectural o.g.f.: x^2*(1 + 3*x + x^2 + x^3)/((1 - x^2)^3*(1 - x)^2). - Peter Bala, Aug 15 2014

Conjectural closed form: 64*a(n) = 2*n^2 -16*n/3 -3 +16*n^3/3 +2*n^4 +(-1)^n *(3-2*n^2). - R. J. Mathar, Oct 01 2016

Mathematica

f[k_] := Floor[(k + 1)/2]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 50}]  (* A203246 *)

Crossrefs

Cf. A203298, A203299, A246117, A212523 (bisection ?), A103220 (bisection?)

Sequence in context: A271997 A360312 A332368 * A106985 A238742 A023261

Adjacent sequences: A203243 A203244 A203245 * A203247 A203248 A203249

Keyword

nonn

Author

Clark Kimberling, Dec 31 2011

Status

approved