%I #21 Jan 05 2023 10:18:32

%S 1,2,5,12,27,62,141,320,727,1650,3745,8500,19291,43782,99365,225512,

%T 511807,1161562,2636201,5982940,13578467,30816750,69939565,158730000,

%U 360242631,817581762,1855527025,4211175812,9557393387,21690799062,49227937461,111724322360

%N Expansion of (1-x)^(-1)/(1-x-2*x^2-2*x^3).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,0,-2).

%F a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3) + 1. - _Christian Krause_, Jan 02 2023

%t CoefficientList[Series[(1-x)^(-1)/(1-x-2x^2-2x^3),{x,0,40}],x] (* or *) LinearRecurrence[{2,1,0,-2},{1,2,5,12},40] (* _Harvey P. Dale_, Sep 14 2016 *)

%o (PARI) my(x='x+O('x^40)); Vec((1-x)^(-1)/(1-x-2*x^2-2*x^3)) \\ _Christian Krause_, Jan 02 2023

%Y Cf. A077946 (first differences).

%Y Cf. A078006 (second differences).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 17 2002