A203231 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,1,3,1,3,1,3,1,...).

1, 4, 15, 24, 81, 108, 351, 432, 1377, 1620, 5103, 5832, 18225, 20412, 63423, 69984, 216513, 236196, 728271, 787320, 2421009, 2598156, 7971615, 8503056, 26040609, 27634932, 84499119, 89282088, 272629233, 286978140, 875283327, 918330048

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Formula

Conjecture: a(n) = 6*a(n-2)-9*a(n-4) with G.f. x*(1+4*x+9*x^2) / (-1+3*x^2)^2 . - R. J. Mathar, Oct 15 2013

Mathematica

r = {3, 1, 3, 1, 3, 1};
s = Flatten[{r, r, r, r, r, r, r, r, r}];
t[n_] := Part[s, Range[n]]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 32}]     (* A203231 *)

Crossrefs

Cf. A010684, A203230, A120908 (bisection).

Sequence in context: A054308 A051531 A062835 * A171788 A063129 A061873

Adjacent sequences: A203228 A203229 A203230 * A203232 A203233 A203234

Keyword

nonn

Author

Clark Kimberling, Dec 30 2011

Status

approved