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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 (list; graph; refs; listen; history; text; internal format)
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: A059859 A146617 A245240 * A112561 A303170 A287617

Adjacent sequences:  A203230 A203231 A203232 * A203234 A203235 A203236

KEYWORD

nonn

AUTHOR

Clark Kimberling, Dec 30 2011

STATUS

approved

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Last modified July 5 21:00 EDT 2020. Contains 335473 sequences. (Running on oeis4.)