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

Author

Clark Kimberling, Dec 30 2011

Keywords

• nonn

Crossrefs

Cf. A010684, A203230, A120908 (bisection).

Programs

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 *)

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