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%I #15 Sep 08 2022 08:45:28
%S 1,4,16,58,208,740,2628,9327,33096,117432,416668,1478400,5245576,
%T 18612052,66038209,234312956,831375680,2949839102,10466448480,
%U 37136447100,131765393560,467522347871,1658835752336,5885785066224,20883602126968,74097989119616
%N Expansion of g.f.: x/((1-x^2)^4 -1+x).
%H G. C. Greubel, <a href="/A123889/b123889.txt">Table of n, a(n) for n = 0..1000</a>
%H A. Burstein and T. Mansour, <a href="https://arxiv.org/abs/math/0112281">Words restricted by 3-letter ...</a>, arXiv:math/0112281 [math.CO], 2001.
%H A. Burstein and T. Mansour, <a href="https://doi.org/10.1007/s000260300000">Words Restricted by 3-Letter Generalized Multipermutation Patterns</a>, Annals. Combin., 7 (2003), 1-14.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,-6,0,4,0,-1).
%p seq(coeff(series(1/(1-4*x+6*x^3-4*x^5+x^7), x, n+1), x, n), n = 0 .. 30); # _G. C. Greubel_, Aug 07 2019
%t CoefficientList[Series[x/((1-x^2)^4 -1+x), {x,0,30}], x] (* _G. C. Greubel_, Aug 07 2019 *)
%o (PARI) my(x='x+O('x^30)); Vec(x/((1-x^2)^4 -1+x)) \\ _G. C. Greubel_, Aug 07 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x/((1-x^2)^4 -1+x) )); // _G. C. Greubel_, Aug 07 2019
%o (Sage)
%o def A123889_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( x/((1-x^2)^4 -1+x) ).list()
%o A123889_list(30) # _G. C. Greubel_, Aug 07 2019
%o (GAP) a:=[1,4,16,58,208,740,2628];; for n in [8..30] do a[n]:=4*a[n-1] -6*a[n-3] +4*a[n-5]-a[n-7]; od; a; # _G. C. Greubel_, Aug 07 2019
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Nov 20 2006
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