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A203246 Second elementary symmetric function of the first n terms of (1,1,2,2,3,3,4,4,...). 5
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 (list; graph; refs; listen; history; text; internal format)
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: A234372 A102725 A271997 * A106985 A238742 A023261

Adjacent sequences:  A203243 A203244 A203245 * A203247 A203248 A203249

KEYWORD

nonn

AUTHOR

Clark Kimberling, Dec 31 2011

STATUS

approved

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Last modified December 7 05:39 EST 2016. Contains 278841 sequences.