A203241 - OEIS

%I #21 Mar 22 2018 09:49:35

%S 2,14,70,310,1302,5334,21590,86870,348502,1396054,5588310,22361430,

%T 89462102,357881174,1431590230,5726491990,22906230102,91625444694,

%U 366502827350,1466013406550,5864057820502,23456239670614,93824975459670

%N Second elementary symmetric function of the first n terms of (1,2,4,8,...).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).

%F a(n) = 2*A006095(n).

%F From _Colin Barker_, Aug 15 2014: (Start)

%F a(n) = (2 - 3*2^n + 4^n)/3.

%F a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3).

%F G.f.: -2*x^2 / ((x-1)*(2*x-1)*(4*x-1)). (End)

%F a(n) = Sum_{k=0...n-2} 2^k*(2^(n-1)-1+2^k). - _J. M. Bergot_, Mar 21 2018

%t f[k_] := 2^(k - 1); t[n_] := Table[f[k], {k, 1, n}]

%t a[n_] := SymmetricPolynomial[2, t[n]]

%t Table[a[n], {n, 2, 32}]    (* A203241 *)

%t Table[a[n]/2, {n, 2, 32}]  (* A006095 *)

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

%Y Cf. A006095.

%K nonn,easy

%O 2,1

%A _Clark Kimberling_, Dec 31 2011