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, 103411, 113575

Offset

2,2

Comments

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

Links

Table of n, a(n) for n=2..43.

Sela Fried, On A203246, 2024.

Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

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

Both conjectures are true. See link. - Sela Fried, Dec 22 2024

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 (odd bisection), A103220 (even bisection).

Sequence in context: A271997 A360312 A332368 * A106985 A238742 A023261

Adjacent sequences: A203243 A203244 A203245 * A203247 A203248 A203249

Keyword

nonn,easy

Author

Clark Kimberling, Dec 31 2011

Status

approved