A203232 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (2,3,2,3,2,3,...).
1, 5, 16, 60, 156, 540, 1296, 4320, 9936, 32400, 72576, 233280, 513216, 1632960, 3545856, 11197440, 24074496, 75582720, 161243136, 503884800, 1068235776, 3325639680, 7014076416, 21767823360, 45712429056, 141490851840
Offset: 1
Keywords
Crossrefs
Cf. A203233.
Programs
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Mathematica
r = {2, 3, 2, 3, 2, 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, 32}] (* A203232 *)
Formula
Conjecture: a(n)=12*a(n-2)-36*a(n-4) with G.f. x*(1+x)*(4*x+1) / (-1+6*x^2)^2 . - R. J. Mathar, Oct 15 2013