login
Expansion of x*(2 - 7*x + 2*x^2)/((1-x)*(1-4*x)*(1-2*x)).
0

%I #25 Sep 06 2024 16:55:34

%S 2,7,23,79,287,1087,4223,16639,66047,263167,1050623,4198399,16785407,

%T 67125247,268468223,1073807359,4295098367,17180131327,68720001023,

%U 274878955519,1099513724927,4398050705407,17592194433023,70368760954879

%N Expansion of x*(2 - 7*x + 2*x^2)/((1-x)*(1-4*x)*(1-2*x)).

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

%F a(n) = 2^(2*n - 1) + 2*a(n - 1) + 1.

%F From _R. J. Mathar_, Jun 13 2008: (Start)

%F O.g.f.: x*(2 - 7*x + 2*x^2)/((1-x)*(1-4*x)*(1-2*x)).

%F a(n) = A093069(n-2), n>1. (End)

%t f[n_Integer?Positive] := f[n] = 2^(2*n - 1) + 2*f[n - 1] + 1; f[0] = 2; Table[f[n], {n, 0, 30}]

%t CoefficientList[Series[x*(2-7x+2x^2)/((1-x)(1-4x)(1-2x)),{x,0,30}],x] (* _Harvey P. Dale_, Sep 07 2015 *)

%Y Cf. A093069, A099393, A028244.

%K nonn,easy

%O 1,1

%A _Roger L. Bagula_, Aug 09 2007

%E New name from _Joerg Arndt_, Feb 08 2015