A097553 - OEIS

%I #14 Apr 20 2021 06:48:53

%S 1,6,27,101,346,1131,3611,11396,35761,111906,349700,1092039,3409031,

%T 10640179,33206991,103631414,323402952,1009233980,3149469548,

%U 9828376731,30670834516,95712596642,298684343689,932085486213,2908700435744

%N Number of positive words of length n in the monoid Br_6 of positive braids on 7 strands.

%H G. C. Greubel, <a href="/A097553/b097553.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,17,-17,11,-5,1).

%F G.f.: (1 +x^2)^4/(1 -6*x +13*x^2 -17*x^3 +17*x^4 -11*x^5 +5*x^6 -x^7).

%t CoefficientList[Series[(1+n^2)^4/(1-6n+13n^2-17n^3+17n^4-11n^5+5n^6-n^7),{n,0,30}],n] (* _Harvey P. Dale_, Sep 27 2019 *)

%t LinearRecurrence[{6,-13,17,-17,11,-5,1}, {1,6,27,101,346,1131,3611,11396,35761}, 40] (* _G. C. Greubel_, Apr 20 2021 *)

%o (Magma)

%o R<x>:=PowerSeriesRing(Integers(), 50);

%o Coefficients(R!( (1+x^2)^4/(1-6*x+13*x^2-17*x^3+17*x^4-11*x^5+5*x^6-x^7) )); // _G. C. Greubel_, Apr 20 2021

%o (Sage)

%o def A097553_list(prec):

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

%o     return P( (1+x^2)^4/(1-6*x+13*x^2-17*x^3+17*x^4-11*x^5+5*x^6-x^7) ).list()

%o A097553_list(50) # _G. C. Greubel_, Apr 20 2021

%Y Cf. A097550, A097551, A097552, A097554, A097555, A097556.

%K nonn,easy

%O 0,2

%A _D n Verma_, Aug 16 2004

%E Corrected and extended by _Max Alekseyev_, Jun 17 2011