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%I #29 Mar 20 2023 15:17:32
%S 0,0,0,0,2,3,8,16,36,76,164,348,740,1564,3300,6940,14564,30492,63716,
%T 132892,276708,575260,1194212,2475804,5126372,10602268,21903588,
%U 45205276,93206756,192005916,395196644,812762908,1670265060,3430008604,7038974180,14435862300
%N Expansion of x^4*(2-3*x-x^2)/((1+x)*(1-2*x)^2).
%H Vincenzo Librandi, <a href="/A219751/b219751.txt">Table of n, a(n) for n = 0..1000</a>
%H M. H. Albert, M. D. Atkinson and Robert Brignall, <a href="http://arxiv.org/abs/1206.3183">The enumeration of three pattern classes</a>, arXiv:1206.3183 [math.CO], (2012), p. 14 (Lemma 4.3).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-4).
%F G.f.: x^4*(2-3*x-x^2)/((1+x)*(1-2*x)^2).
%F a(n) = (2^(n-5)*(3*n+16)+4*(-1)^n)/9 with n>3, a(0)=a(1)=a(2)=a(3)=0. [_Bruno Berselli_, Nov 29 2012]
%t CoefficientList[Series[x^4 (2 - 3 x - x^2)/((1 + x) (1 - 2 x)^2), {x, 0, 35}], x] (* _Bruno Berselli_, Nov 30 2012 *)
%o (Maxima) makelist(coeff(taylor(x^4*(2-3*x-x^2)/((1+x)*(1-2*x)^2), x, 0, n), x, n), n, 0, 35); /* _Bruno Berselli_, Nov 29 2012 */
%o (Magma) I:=[0, 0, 0, 0, 2, 3, 8]; [n le 7 select I[n] else 3*Self(n-1) - 4*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Dec 14 2012
%Y Cf. A219752-A219759, A219837.
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_, Nov 28 2012
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