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A203161 (n-1)-st elementary symmetric function of the first n terms of  (3,1,2,3,1,2,3,1,2,...). 2
1, 4, 11, 39, 57, 132, 432, 540, 1188, 3780, 4428, 9504, 29808, 33696, 71280, 221616, 244944, 513216, 1586304, 1726272, 3592512, 11057472, 11897280, 24634368, 75582720, 80621568, 166281984, 508923648, 539156736, 1108546560, 3386105856 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From R. J. Mathar, Oct 01 2016 (Start):

The k-th elementary symmetric functions of the first n terms of 3,1,2,3,1,2.., form a triangle T(n,k), 0<=k<=n, n>=0:

1

1 3

1 4 3

1 6 11 6

1 9 29 39 18

1 10 38 68 57 18

1 12 58 144 193 132 36

1 15 94 318 625 711 432 108

1 16 109 412 943 1336 1143 540 108

1 18 141 630 1767 3222 3815 2826 1188 216

1 21 195 1053 3657 8523 13481 14271 9666 3780 648

This here is the first subdiagonal. The diagonal is a stuttered version of A026532. The 2nd column is A047231 (or A144429). (End)

LINKS

Table of n, a(n) for n=1..31.

Index entries for linear recurrences with constant coefficients, signature (0,0,12,0,0,-36).

FORMULA

G.f.: x*(3*x+1)*(3*x^3+8*x^2+x+1) / (6*x^3-1)^2. - Colin Barker, Aug 15 2014

EXAMPLE

Let esf abbreviate "elementary symmetric function".  Then

0th esf of {3}:  1,

1st esf of {3,1}:  3+1=4,

2nd esf of {3,1,2} is 3*1+3*1+1*2=11.

MATHEMATICA

f[k_] := 1 + Mod[k + 1, 3]; t[n_] := Table[f[k], {k, 1, n}]

a[n_] := SymmetricPolynomial[n - 1, t[n]]

Table[a[n], {n, 1, 33}] (* A203161 *)

PROG

(PARI) Vec(x*(3*x+1)*(3*x^3+8*x^2+x+1)/(6*x^3-1)^2 + O(x^100)) \\ Colin Barker, Aug 15 2014

CROSSREFS

Cf. A010882, A203160, A203162.

Sequence in context: A149256 A149257 A255706 * A050987 A137191 A106269

Adjacent sequences:  A203158 A203159 A203160 * A203162 A203163 A203164

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Dec 29 2011

STATUS

approved

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Last modified May 24 18:34 EDT 2019. Contains 323534 sequences. (Running on oeis4.)