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

1,2

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*(36*x^4+16*x^3+11*x^2+5*x+1) / (6*x^3-1)^2. - Colin Barker, Aug 15 2014

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A010882, A203162.

Sequence in context: A181896 A041671 A215221 * A095053 A291279 A182379

Adjacent sequences: A203157 A203158 A203159 * A203161 A203162 A203163

Keyword

nonn,easy

Author

Clark Kimberling, Dec 29 2011

Status

approved