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

1,2

Links

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

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

Adjacent sequences: A203230 A203231 A203232 * A203234 A203235 A203236

Keyword

nonn

Author

Clark Kimberling, Dec 30 2011

Status

approved