%I #31 Feb 14 2024 05:19:36

%S 0,0,0,0,1,2,4,9,18,39,80,169,350,731,1516,3149,6522,13503,27912,

%T 57649,118934,245155,504868,1038869,2135986,4388487,9009984,18486009,

%U 37904078,77672299,159072860,325602269,666117610,1362061391,2783775096,5686854849,11612318982

%N Expansion of x^4*(1-3*x^2-x^3)/((1+x)*(1-2*x)*(1-x-2*x^2)).

%H Vincenzo Librandi, <a href="/A219755/b219755.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. 17 (Lemma 4.6).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-4,-4).

%F G.f.: x^4*(1-3*x^2-x^3)/((1+x)*(1-2*x)*(1-x-2*x^2)).

%F a(n) = (2^(n-5)*(3*n+38)-(3*n-14)*(-1)^n)/27 with n>3, a(0)=a(1)=a(2)=a(3)=0. [_Bruno Berselli_, Nov 29 2012]

%t CoefficientList[Series[x^4 (1 - 3 x^2 - x^3)/((1 + x) (1 - 2 x) (1 - x - 2 x^2)), {x, 0, 36}], x] (* _Bruno Berselli_, Nov 30 2012 *)

%o (Maxima) makelist(coeff(taylor(x^4*(1-3*x^2-x^3)/((1+x)*(1-2*x)*(1-x-2*x^2)), x, 0, n), x, n), n, 0, 36); /* _Bruno Berselli_, Nov 29 2012 */

%o (Magma) I:=[0, 0, 0, 0, 1, 2, 4, 9]; [n le 8 select I[n] else 2*Self(n-1) + 3*Self(n-2) - 4*Self(n-3) - 4*Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Dec 15 2012

%Y Cf. A219751-A219759, A219837.

%K nonn,easy

%O 0,6

%A _N. J. A. Sloane_, Nov 28 2012