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A203298 Second elementary symmetric function of the first n terms of (1,2,2,3,3,4,4,5,5...). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 18 22:26 EDT 2019. Contains 328211 sequences. (Running on oeis4.)