A203167 (n-1)-st elementary symmetric function of the first n terms of (2,2,1,2,2,1,2,2,1,...)=(A130196 for n>0).

1, 4, 8, 20, 48, 64, 144, 320, 384, 832, 1792, 2048, 4352, 9216, 10240, 21504, 45056, 49152, 102400, 212992, 229376, 475136, 983040, 1048576, 2162688, 4456448, 4718592, 9699328, 19922944, 20971520, 42991616, 88080384, 92274688, 188743680

Offset: 1

Author

Clark Kimberling, Dec 30 2011

Keywords

• nonn

Crossrefs

Cf. A130196, A058582.

Programs

Mathematica

f[k_] := 1 + Mod[k^2, 3]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 33}]  (* A203167 *)

Formula

From R. J. Mathar, Jul 02 2013: (Start)

Conjecture: a(n) = 8*a(n-3) - 16*a(n-6).

Conjecture: G.f.: x*(1+4*x+8*x^2+12*x^3+16*x^4) / (-1+4*x^3)^2.

(End)