A203235 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (1,1,1,3,1,1,1,3,...).

1, 2, 3, 10, 13, 16, 19, 60, 69, 78, 87, 270, 297, 324, 351, 1080, 1161, 1242, 1323, 4050, 4293, 4536, 4779, 14580, 15309, 16038, 16767, 51030, 53217, 55404, 57591, 174960, 181521, 188082, 194643, 590490, 610173, 629856, 649539, 1968300

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Formula

Conjecture: a(n) = 6*a(n-4)-9*a(n-8) with G.f. x*(1+2*x+3*x^2+10*x^3+7*x^4+4*x^5+x^6) / ( (-1+3*x^4)^2 ). - R. J. Mathar, Oct 15 2013

Mathematica

r = {1, 1, 1, 3, 1, 1, 1, 3};
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, 47}]     (* A203235 *)

Crossrefs

Cf. A203234.

Sequence in context: A218028 A067769 A066089 * A256214 A256213 A256414

Adjacent sequences: A203232 A203233 A203234 * A203236 A203237 A203238

Keyword

nonn

Author

Clark Kimberling, Dec 30 2011

Status

approved