A097554 - OEIS

%I #11 Apr 20 2021 06:49:00

%S 1,7,36,151,570,2019,6893,23034,76020,249077,812614,2644447,8592693,

%T 27895296,90510106,293576779,952053411,3087093728,10009389358,

%U 32452403488,105214363653,341111617862,1105895184121,3585328906357,11623651559099

%N Number of positive words of length n in the monoid Br_7 of positive braids on 8 strands.

%H G. C. Greubel, <a href="/A097554/b097554.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 (7,-18,25,-24,15,-6,1).

%F G.f.: (1 +x^2)^5/(1 -7*x +18*x^2 -25*x^3 +24*x^4 -15*x^5 +6*x^6 -x^7).

%t LinearRecurrence[{7,-18,25,-24,15,-6,1}, {1,7,36,151,570,2019,6893,23034,76020, 249077,812614}, 41] (* _G. C. Greubel_, Apr 20 2021 *)

%o (Magma)

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

%o Coefficients(R!( (1+x^2)^5/(1-7*x+18*x^2-25*x^3+24*x^4-15*x^5+6*x^6-x^7) )); // _G. C. Greubel_, Apr 20 2021

%o (Sage)

%o def A097554_list(prec):

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

%o     return P( (1+x^2)^5/(1-7*x+18*x^2-25*x^3+24*x^4-15*x^5+6*x^6-x^7) ).list()

%o A097554_list(40) # _G. C. Greubel_, Apr 20 2021

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