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Number of positive words of length n in the monoid Br_5 of positive braids on 6 strands.
7

%I #13 Apr 20 2021 00:58:51

%S 1,5,20,67,209,630,1873,5540,16357,48265,142387,420027,1239006,

%T 3654820,10780958,31801551,93807834,276713194,816245143,2407749755,

%U 7102350204,20950424039,61799299470,182294802589,537730934397

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

%H G. C. Greubel, <a href="/A097552/b097552.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,7,-4,1).

%F 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 LinearRecurrence[{5,-8,7,-4,1}, {1,5,20,67,209,630,1873}, 40] (* _G. C. Greubel_, Apr 19 2021 *)

%o (Magma)

%o R<x>:=PowerSeriesRing(Integers(), 40);

%o 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 (Sage)

%o def A097552_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( (1+x^2)^3/(1-5*x+8*x^2-7*x^3+4*x^4-x^5) ).list()

%o A097552_list(40) # _G. C. Greubel_, Apr 19 2021

%Y Cf. A097550, A097551, A097553, A097554, A097555, A097556.

%K nonn,easy

%O 0,2

%A _D n Verma_, Aug 16 2004

%E Corrected by _T. D. Noe_, Nov 02 2006