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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.

%I A203160 #22 Feb 18 2025 03:54:56
%S A203160 1,5,11,28,96,132,300,972,1188,2592,8208,9504,20304,63504,71280,
%T A203160 150336,466560,513216,1073088,3312576,3592512,7464960,22954752,
%U A203160 24634368,50948352,156204288,166281984,342641664,1048080384,1108546560,2277559296
%N A203160 (n-1)-st elementary symmetric function of the first n terms of (2,3,1,2,3,1,2,3,1,...)=A010882.
%H A203160 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,12,0,0,-36).
%F A203160 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 A203160 Let esf abbreviate "elementary symmetric function".  Then
%e A203160 0th esf of {2}:  1,
%e A203160 1st esf of {2,3}:  2+3=5,
%e A203160 2nd esf of {2,3,1} is 2*3+2*1+3*1=11.
%t A203160 f[k_] := 1 + Mod[k, 3]; t[n_] := Table[f[k], {k, 1, n}]
%t A203160 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A203160 Table[a[n], {n, 1, 33}] (* A203160 *)
%t A203160 LinearRecurrence[{0,0,12,0,0,-36},{1,5,11,28,96,132},40] (* _Harvey P. Dale_, Mar 19 2016 *)
%o A203160 (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 A203160 Cf. A010882, A203162.
%K A203160 nonn,easy
%O A203160 1,2
%A A203160 _Clark Kimberling_, Dec 29 2011