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A097551 Number of positive words of length n in the monoid Br_4 of positive braids on 5 strands.

%I A097551 #12 Apr 20 2021 02:38:25
%S A097551 1,4,13,37,101,273,737,1990,5374,14513,39194,105848,285855,771985,
%T A097551 2084836,5630344,15205404,41063976,110898081,299493268,808816679,
%U A097551 2184304257,5898969706,15930859211,43023152830,116189067703
%N A097551 Number of positive words of length n in the monoid Br_4 of positive braids on 5 strands.
%H A097551 G. C. Greubel, <a href="/A097551/b097551.txt">Table of n, a(n) for n = 0..1000</a>
%H A097551 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,5,-3,1).
%F A097551 G.f.: (1 + x^2)^2/(1 - 4*x + 5*x^2 - 5*x^3 + 3*x^4 - x^5).
%t A097551 <<DiscreteMath`; Do[Print[SeriesTerm[(1 + q^2)^2/(1-4q+5q^2-5q^3+3q^4-q^5), {q, 0, n}]], {n, 0, 50}] (* _Ryan Propper_, Sep 27 2005 *)
%t A097551 LinearRecurrence[{4,-5,5,-3,1}, {1,4,13,37,101}, 51] (* _G. C. Greubel_, Apr 19 2021 *)
%o A097551 (Magma)
%o A097551 R<x>:=PowerSeriesRing(Integers(), 50);
%o A097551 Coefficients(R!( (1+x^2)^2/(1-4*x+5*x^2-5*x^3+3*x^4-x^5) )); // _G. C. Greubel_, Apr 19 2021
%o A097551 (Sage)
%o A097551 def A097551_list(prec):
%o A097551     P.<x> = PowerSeriesRing(ZZ, prec)
%o A097551     return P( (1+x^2)^2/(1-4*x+5*x^2-5*x^3+3*x^4-x^5) ).list()
%o A097551 A097551_list(50) # _G. C. Greubel_, Apr 19 2021
%Y A097551 Cf. A097550, A097552, A097553, A097554, A097555, A097556.
%K A097551 nonn,easy
%O A097551 0,2
%A A097551 _D n Verma_, Aug 16 2004
%E A097551 More terms from _Ryan Propper_, Sep 27 2005