%I #23 Feb 11 2023 13:53:12
%S 1,5,15,34,62,90,91,11,-231,-716,-1444,-2172,-2171,17,6579,19702,
%T 39386,59070,59071,23,-177123,-531416,-1062856,-1594296,-1594295,29,
%U 4782999,14348938,28697846,43046754,43046755,35,-129140127,-387420452,-774840940,-1162261428
%N Expansion of g.f. 1/((1 - x)^2*(1 - 3*x + 3*x^2)).
%H Colin Barker, <a href="/A279231/b279231.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,9,-3).
%F a(n) = 5*a(n-1) - 10*a(n-2) + 9*a(n-3) - 3*a(n-4) for n > 3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + n + 1, with a(-1) = a(-2) = 0.
%F a(n) = 4 + n + 3^(1+n/2)*(sqrt(3)*sin(n*Pi/6) - cos(n*Pi/6)). - _Stefano Spezia_, Feb 11 2023
%o (PARI) Vec(1/((1-x)^2*(1-3*x+3*x^2)) + O(x^30)) \\ _Colin Barker_, Dec 08 2016
%Y Cf. A001477, A045618, A077859.
%K sign,easy
%O 0,2
%A _Philippe Deléham_, Dec 08 2016
%E Incorrect term corrected by _Colin Barker_, Dec 09 2016