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A203162 (n-1)-st elementary symmetric function of the first n terms of (1,2,3,1,2,3,1,2,3,...). 6
1, 3, 11, 17, 40, 132, 168, 372, 1188, 1404, 3024, 9504, 10800, 22896, 71280, 79056, 165888, 513216, 559872, 1166400, 3592512, 3872448, 8024832, 24634368, 26313984, 54307584, 166281984, 176359680, 362797056, 1108546560, 1169012736 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

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

FORMULA

a(n) = 12*a(n-3)-36*a(n-6). - Clark Kimberling, Aug 18 2012

G.f.: (1 + 3*x + 11*x^2 + 5*x^3 + 4*x*4)/(1 - 6*x^3)^2. - Clark Kimberling, Aug 18 2012

EXAMPLE

Let esf abbreviate "elementary symmetric function". Then

0th esf of {1}:  1;

1st esf of {1,2}:  1+2=3;

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

MATHEMATICA

f[k_] := 1 + Mod[k + 2, 3]; t[n_] := Table[f[k], {k, n}]; a[n_] := SymmetricPolynomial[n - 1, t[n]]; Table[a[n], {n, 33}] (* A203162 *)

CROSSREFS

Cf. A010882, A203160, A203161.

Sequence in context: A302872 A023865 A024592 * A240084 A100567 A270225

Adjacent sequences:  A203159 A203160 A203161 * A203163 A203164 A203165

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Dec 29 2011

STATUS

approved

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Last modified April 24 04:48 EDT 2019. Contains 322412 sequences. (Running on oeis4.)