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A337654 Expansion of H(x)*(1+x^5)/(1-x^2-x^3-x^4) where H(x) = g.f. for A249665.

%I A337654 #27 Sep 23 2024 04:00:29
%S A337654 0,1,1,2,4,10,22,45,93,197,420,890,1878,3964,8380,17724,37474,79209,
%T A337654 167426,353927,748202,1581668,3343519,7067929,14941121,31584586,
%U A337654 66767743,141142461,298365531,630724607,1333309486,2818526581,5958175175,12595180550,26625362976,56284223827
%N A337654 Expansion of H(x)*(1+x^5)/(1-x^2-x^3-x^4) where H(x) = g.f. for A249665.
%H A337654 G. C. Greubel, <a href="/A337654/b337654.txt">Table of n, a(n) for n = 0..1000</a>
%H A337654 Maria M. Gillespie, Kenneth G. Monks, and Kenneth M. Monks, <a href="https://arxiv.org/abs/1808.03573">Enumerating Anchored Permutations with Bounded Gaps</a>, arXiv:1808.03573 [math.CO], 2018. Also Discrete Math.,343 (2020), #111957. See B(x).
%H A337654 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,1,1,0,-1,-1).
%F A337654 G.f.: x*(1-x+x^2-x^3+x^4)/(1-2*x+x^2-2*x^3-x^4-x^5+x^7+x^8).
%F A337654 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) + a(n-4) + a(n-5) - a(n-7) - a(n-8) for n>7. - _Colin Barker_, Oct 11 2020
%t A337654 LinearRecurrence[{2,-1,2,1,1,0,-1,-1},{0,1,1,2,4,10,22,45},40] (* _Harvey P. Dale_, May 04 2023 *)
%o A337654 (PARI) concat(0, Vec((x^4-x^3+x^2-x+1)*x/(x^8+x^7-x^5-x^4-2*x^3+x^2-2*x+1)+ O(x^40))) \\ _Michel Marcus_, Oct 11 2020
%o A337654 (Magma)
%o A337654 R<x>:=PowerSeriesRing(Integers(), 50);
%o A337654 [0] cat Coefficients(R!( x*(1+x^5)/((1+x)*(1-2*x+x^2-2*x^3-x^4-x^5+x^7+x^8)) )); // _G. C. Greubel_, Sep 23 2024
%o A337654 (SageMath)
%o A337654 def A337654_list(prec):
%o A337654     P.<x> = PowerSeriesRing(ZZ, prec)
%o A337654     return P( x*(1+x^5)/((1+x)*(1-2*x+x^2-2*x^3-x^4-x^5+x^7+x^8)) ).list()
%o A337654 A337654_list(50) # _G. C. Greubel_, Sep 23 2024
%Y A337654 Cf. A249665.
%K A337654 nonn,easy
%O A337654 0,4
%A A337654 _N. J. A. Sloane_, Sep 29 2020