A203243 Second elementary symmetric function of the first n terms of (1,3,9,27,81,...).

3, 39, 390, 3630, 33033, 298389, 2688780, 24208860, 217909263, 1961271939, 17651713170, 158866215690, 1429798332693, 12868192168689, 115813751041560, 1042323823944120, 9380914609207323, 84428232063996639, 759854090319361950

Offset: 2

Author

Clark Kimberling, Dec 31 2011

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (13,-39,27).

Crossrefs

Cf. A006100.

Programs

Mathematica

f[k_] := 3^(k - 1); t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 32}]    (* A203243 *)
Table[a[n]/3, {n, 2, 32}]  (* A006100 *)

PARI

Vec(-3*x^2/((x-1)*(3*x-1)*(9*x-1)) + O(x^100)) \\ Colin Barker, Aug 15 2014

Formula

a(n) = 3*A006100(n).

From Colin Barker, Aug 15 2014: (Start)

a(n) = (3-4*3^n+9^n)/16.

a(n) = 13*a(n-1)-39*a(n-2)+27*a(n-3).

G.f.: -3*x^2 / ((x-1)*(3*x-1)*(9*x-1)). (End)