cp's OEIS Frontend

A097553 Number of positive words of length n in the monoid Br_6 of positive braids on 7 strands.

%I A097553 #14 Apr 20 2021 06:48:53
%S A097553 1,6,27,101,346,1131,3611,11396,35761,111906,349700,1092039,3409031,
%T A097553 10640179,33206991,103631414,323402952,1009233980,3149469548,
%U A097553 9828376731,30670834516,95712596642,298684343689,932085486213,2908700435744
%N A097553 Number of positive words of length n in the monoid Br_6 of positive braids on 7 strands.
%H A097553 G. C. Greubel, <a href="/A097553/b097553.txt">Table of n, a(n) for n = 0..1000</a>
%H A097553 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,17,-17,11,-5,1).
%F A097553 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 A097553 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 A097553 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 A097553 (Magma)
%o A097553 R<x>:=PowerSeriesRing(Integers(), 50);
%o A097553 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 A097553 (Sage)
%o A097553 def A097553_list(prec):
%o A097553     P.<x> = PowerSeriesRing(ZZ, prec)
%o A097553     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 A097553_list(50) # _G. C. Greubel_, Apr 20 2021
%Y A097553 Cf. A097550, A097551, A097552, A097554, A097555, A097556.
%K A097553 nonn,easy
%O A097553 0,2
%A A097553 _D n Verma_, Aug 16 2004
%E A097553 Corrected and extended by _Max Alekseyev_, Jun 17 2011