A203234 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (1,1,1,2,1,1,1,2,...).

1, 2, 3, 7, 9, 11, 13, 28, 32, 36, 40, 84, 92, 100, 108, 224, 240, 256, 272, 560, 592, 624, 656, 1344, 1408, 1472, 1536, 3136, 3264, 3392, 3520, 7168, 7424, 7680, 7936, 16128, 16640, 17152, 17664, 35840, 36864, 37888, 38912, 78848, 80896

Offset

1,2

Links

Table of n, a(n) for n=1..45.

Formula

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

Mathematica

r = {1, 1, 1, 2, 1, 1, 1, 2};
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, 45}]     (* A203234 *)

Crossrefs

Cf. A203235.

Sequence in context: A294263 A345745 A280110 * A212985 A103797 A262814

Adjacent sequences: A203231 A203232 A203233 * A203235 A203236 A203237

Keyword

nonn

Author

Clark Kimberling, Dec 30 2011

Status

approved