A203233 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,2,3,2,3,2,...).

1, 5, 21, 60, 216, 540, 1836, 4320, 14256, 32400, 104976, 233280, 746496, 1632960, 5178816, 11197440, 35271936, 75582720, 236825856, 503884800, 1572120576, 3325639680, 10339716096, 21767823360, 67480252416, 141490851840

Offset: 1

Author

Clark Kimberling, Dec 30 2011

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..2559

Crossrefs

Cf. A203232, A212700 (bisection)

Programs

Maple

f:= proc(n) if n::even then (5/12)*n*6^(n/2) else (5*n-1)*6^((n+1)/2)/24 fi
end proc:
map(f, [$1..100]); # Robert Israel, May 04 2017

Mathematica

r = {3, 2, 3, 2, 3, 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, 32}]     (* A203233 *)

Formula

Conjecture: a(n)=12*a(n-2)-36*a(n-4) with G.f. x*(1+5*x+9*x^2) / (-1+6*x^2)^2 . - R. J. Mathar, Oct 15 2013, verified by Robert Israel, May 04 2017

a(n) = (5/12)*n*6^(n/2) if n is even, (5*n-1)*6^((n+1)/2)/24 if n is odd. - Robert Israel, May 04 2017