cp's OEIS Frontend

A169404 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169404 #21 Jul 21 2020 16:32:19
%S A169404 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A169404 423263232,2539579392,15237476352,91424858112,548549148672,
%U A169404 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073472
%N A169404 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169404 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A169404 First disagreement is at index 32, the difference is 21. - _Klaus Brockhaus_, Jun 26 2011
%C A169404 Computed with Magma using commands similar to those used to compute A154638.
%H A169404 Vincenzo Librandi, <a href="/A169404/b169404.txt">Table of n, a(n) for n = 0..165</a>
%H A169404 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).
%F A169404 G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^32 - 5*t^31 - 5*t^30 - 5*t^29 - 5*t^28 - 5*t^27 - 5*t^26 - 5*t^25 - 5*t^24 - 5*t^23 - 5*t^22 - 5*t^21 - 5*t^20 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
%F A169404 G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-5*sum(k=1..31,x^k)+15*x^32).
%t A169404 coxG[{32,15,-5}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 21 2020 *)
%o A169404 (PARI) x='x+O('x^66); /* that many terms */
%o A169404 Vec((1+2*sum(k=1,31,x^k)+x^32)/(1-5*sum(k=1,31,x^k)+15*x^32))   /* show terms */
%o A169404 /* _Joerg Arndt_, Jun 26 2011 */
%Y A169404 Cf. A003949 (G.f.: (1+x)/(1-6*x) ).
%K A169404 nonn,easy
%O A169404 0,2
%A A169404 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009