cp's OEIS Frontend

A097552 Number of positive words of length n in the monoid Br_5 of positive braids on 6 strands.

%I A097552 #13 Apr 20 2021 00:58:51
%S A097552 1,5,20,67,209,630,1873,5540,16357,48265,142387,420027,1239006,
%T A097552 3654820,10780958,31801551,93807834,276713194,816245143,2407749755,
%U A097552 7102350204,20950424039,61799299470,182294802589,537730934397
%N A097552 Number of positive words of length n in the monoid Br_5 of positive braids on 6 strands.
%H A097552 G. C. Greubel, <a href="/A097552/b097552.txt">Table of n, a(n) for n = 0..1000</a>
%H A097552 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,7,-4,1).
%F A097552 G.f.: (1 + x^2)^3/(1 - 5*x + 8*x^2 - 7*x^3 + 4*x^4 - x^5). - _T. D. Noe_, Nov 02 2006
%t A097552 LinearRecurrence[{5,-8,7,-4,1}, {1,5,20,67,209,630,1873}, 40] (* _G. C. Greubel_, Apr 19 2021 *)
%o A097552 (Magma)
%o A097552 R<x>:=PowerSeriesRing(Integers(), 40);
%o A097552 Coefficients(R!( (1+x^2)^3/(1-5*x+8*x^2-7*x^3+4*x^4-x^5) )); // _G. C. Greubel_, Apr 19 2021
%o A097552 (Sage)
%o A097552 def A097552_list(prec):
%o A097552     P.<x> = PowerSeriesRing(ZZ, prec)
%o A097552     return P( (1+x^2)^3/(1-5*x+8*x^2-7*x^3+4*x^4-x^5) ).list()
%o A097552 A097552_list(40) # _G. C. Greubel_, Apr 19 2021
%Y A097552 Cf. A097550, A097551, A097553, A097554, A097555, A097556.
%K A097552 nonn,easy
%O A097552 0,2
%A A097552 _D n Verma_, Aug 16 2004
%E A097552 Corrected by _T. D. Noe_, Nov 02 2006