A203160 (n-1)-st elementary symmetric function of the first n terms of (2,3,1,2,3,1,2,3,1,...)=A010882.
1, 5, 11, 28, 96, 132, 300, 972, 1188, 2592, 8208, 9504, 20304, 63504, 71280, 150336, 466560, 513216, 1073088, 3312576, 3592512, 7464960, 22954752, 24634368, 50948352, 156204288, 166281984, 342641664, 1048080384, 1108546560, 2277559296
Offset: 1
Examples
Let esf abbreviate "elementary symmetric function". Then
0th esf of {2}: 1,
1st esf of {2,3}: 2+3=5,
2nd esf of {2,3,1} is 2*3+2*1+3*1=11.
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,12,0,0,-36).
Programs
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Mathematica
f[k_] := 1 + Mod[k, 3]; t[n_] := Table[f[k], {k, 1, n}] a[n_] := SymmetricPolynomial[n - 1, t[n]] Table[a[n], {n, 1, 33}] (* A203160 *) LinearRecurrence[{0,0,12,0,0,-36},{1,5,11,28,96,132},40] (* Harvey P. Dale, Mar 19 2016 *) -
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
Formula
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