%I #4 Sep 14 2017 18:15:05

%S 1,3,8,21,54,136,337,825,2000,4809,11484,27264,64401,151455,354808,

%T 828349,1927986,4475080,10361441,23936565,55183904,126983569,

%U 291698040,669004352,1532095329,3503889147,8003207912,18258464741,41608726254,94722900936,215428701233

%N a(n) = (1/4)*A291038(n).

%H Clark Kimberling, <a href="/A291039/b291039.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4, -4, 2, -4, 0, -1)

%F G.f.: -((-1 + x + x^3)/(-1 + 2 x + x^3)^2).

%F a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-3) - 4*a(n-4) - a(n-6) for n >= 7.

%t z = 60; s = x/(x - x^3); p = (1 - 2 s)^2;

%t Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A079978 *)

%t u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A291038 *)

%t u/4 (* A291039 *)

%Y Cf. A079978, A290616, A291038.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Sep 14 2017