The On-Line Encyclopedia of Integer Sequences (OEIS)

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A203231

(n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,1,3,1,3,1,3,1,...).
(history; published version)

#8 by R. J. Mathar at Tue Oct 15 14:19:18 EDT 2013

STATUS

editing

approved

#7 by R. J. Mathar at Tue Oct 15 14:19:00 EDT 2013

CROSSREFS

Cf. A010684, A203230, A120908 (bisection).

#6 by R. J. Mathar at Tue Oct 15 14:17:56 EDT 2013

FORMULA

Conjecture: a(n) = 6*a(n-2)-9*a(n-4) with G.f. x*(1+4*x+9*x^2) / (-1+3*x^2)^2 . - R. J. Mathar, Oct 15 2013

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:58:05 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Dec 30 2011

Discussion

Fri Mar 30

18:58

OEIS Server: https://oeis.org/edit/global/285

#4 by T. D. Noe at Mon Jan 02 19:44:10 EST 2012

STATUS

proposed

approved

#3 by Clark Kimberling at Mon Jan 02 18:36:03 EST 2012

STATUS

editing

proposed

#2 by Clark Kimberling at Fri Dec 30 17:15:09 EST 2011

NAME

allocated for Clark Kimberling(n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,1,3,1,3,1,3,1,...).

DATA

1, 4, 15, 24, 81, 108, 351, 432, 1377, 1620, 5103, 5832, 18225, 20412, 63423, 69984, 216513, 236196, 728271, 787320, 2421009, 2598156, 7971615, 8503056, 26040609, 27634932, 84499119, 89282088, 272629233, 286978140, 875283327, 918330048

OFFSET

1,2

MATHEMATICA

r = {3, 1, 3, 1, 3, 1};

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}] (* A203231 *)

CROSSREFS

Cf. A010684, A203230.

KEYWORD

allocated

nonn

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Dec 30 2011

STATUS

approved

editing

#1 by Clark Kimberling at Fri Dec 30 09:46:22 EST 2011

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved