login
A203233
(n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,2,3,2,3,2,...).
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
1,2
LINKS
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
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 *)
CROSSREFS
Cf. A203232, A212700 (bisection)
Sequence in context: A146617 A245240 A370839 * A112561 A303170 A287617
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 30 2011
STATUS
approved