Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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