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A203160 (n-1)-st elementary symmetric function of the first n terms of (2,3,1,2,3,1,2,3,1,...)=A010882. 3

%I

%S 1,5,11,28,96,132,300,972,1188,2592,8208,9504,20304,63504,71280,

%T 150336,466560,513216,1073088,3312576,3592512,7464960,22954752,

%U 24634368,50948352,156204288,166281984,342641664,1048080384,1108546560,2277559296

%N (n-1)-st elementary symmetric function of the first n terms of (2,3,1,2,3,1,2,3,1,...)=A010882.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,12,0,0,-36).

%F G.f.: x*(36*x^4+16*x^3+11*x^2+5*x+1) / (6*x^3-1)^2. - _Colin Barker_, Aug 15 2014

%e Let esf abbreviate "elementary symmetric function". Then

%e 0th esf of {2}: 1,

%e 1st esf of {2,3}: 2+3=5,

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

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

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

%t Table[a[n], {n, 1, 33}] (* A203160 *)

%t LinearRecurrence[{0,0,12,0,0,-36},{1,5,11,28,96,132},40] (* _Harvey P. Dale_, Mar 19 2016 *)

%o (PARI) Vec(x*(36*x^4+16*x^3+11*x^2+5*x+1)/(6*x^3-1)^2 + O(x^100)) \\ _Colin Barker_, Aug 15 2014

%Y Cf. A010882, A203162.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Dec 29 2011

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Last modified June 25 09:48 EDT 2019. Contains 324347 sequences. (Running on oeis4.)