A097555 - OEIS

%I #11 Apr 20 2021 06:49:06

%S 1,8,45,205,831,3133,11294,39585,136302,464026,1568151,5273999,

%T 17681042,59149925,197598856,659479754,2199585548,7333198205,

%U 24441067317,81444567492,271360676916,904051477063,3011711782025,10032660556567,33420042561972

%N Number of positive words of length n in the monoid Br_8 of positive braids on 9 strands.

%H G. C. Greubel, <a href="/A097555/b097555.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (8,-25,45,-59,57,-41,21,-7,1).

%F G.f.: (1 +x^2)^6 /(1 -8*x +25*x^2 -45*x^3 +59*x^4 -57*x^5 +41*x^6 -21*x^7 +7*x^8 -x^9).

%t LinearRecurrence[{8,-25,45,-59,57,-41,21,-7,1}, {1,8,45,205,831,3133,11294,39585, 136302, 464026, 1568151, 5273999, 17681042}, 41] (* _G. C. Greubel_, Apr 20 2021 *)

%o (Magma)

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

%o Coefficients(R!( (1+x^2)^6 /(1-8*x+25*x^2-45*x^3+59*x^4-57*x^5+41*x^6-21*x^7+7*x^8-x^9) )); // _G. C. Greubel_, Apr 20 2021

%o (Sage)

%o def A097555_list(prec):

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

%o     return P( (1+x^2)^6 /(1-8*x+25*x^2-45*x^3+59*x^4-57*x^5+41*x^6-21*x^7+7*x^8-x^9) ).list()

%o A097555_list(40) # _G. C. Greubel_, Apr 20 2021

%Y Cf. A097550, A097551, A097552, A097553, A097554, A097556.

%K nonn,easy

%O 0,2

%A _D n Verma_, Aug 16 2004

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