%I #29 Feb 14 2024 05:17:11

%S 0,0,0,0,2,17,90,383,1436,4958,16159,50480,152690,450343,1301764,

%T 3701990,10387887,28827688,79265482,216271927,586261980,1580524894,

%U 4241295935,11336890720,30202962402,80239307847,212664541940,562513804438,1485379408591,3916726647768

%N Expansion of x^4*(2-7*x+6*x^2+x^3-x^4)/((1-x)*(1-2*x)^4*(1-3*x+x^2)).

%H Vincenzo Librandi, <a href="/A219757/b219757.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. 25.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (12,-60,161,-248,216,-96,16).

%F G.f.: x^4*(2-7*x+6*x^2+x^3-x^4)/((1-x)*(1-2*x)^4*(1-3*x+x^2)).

%t CoefficientList[Series[x^4(2-7x+6x^2+x^3-x^4)/((1-x)(1-2x)^4(1-3x+x^2)),{x,0,40}],x] (* _Harvey P. Dale_, Nov 29 2012 *)

%o (Maxima) makelist(coeff(taylor(x^4*(2-7*x+6*x^2+x^3-x^4)/((1-x)*(1-2*x)^4*(1-3*x+x^2)), x, 0, n), x, n), n, 0, 29); /* _Bruno Berselli_, Nov 29 2012 */

%o (Magma) I:=[0, 0, 0, 0, 2, 17, 90, 383, 1436, 4958]; [n le 10 select I[n] else 12*Self(n-1) - 60*Self(n-2) + 161*Self(n-3) - 248*Self(n-4) + 216*Self(n-5) - 96*Self(n-6) + 16*Self(n-7): n in [1..30]]; // _Vincenzo Librandi_, Dec 14 2012

%Y Cf. A219751-A219759, A219837.

%K nonn,easy

%O 0,5

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