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A169402 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169402 #16 May 08 2018 02:39:31
%S A169402 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A169402 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A169402 343597383680,1374389534720,5497558138880,21990232555520,87960930222080
%N A169402 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169402 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A169402 First disagreement is at index 32, the difference is 10. - _Klaus Brockhaus_, Jun 26 2011
%C A169402 Computed with Magma using commands similar to those used to compute A154638.
%H A169402 Vincenzo Librandi, <a href="/A169402/b169402.txt">Table of n, a(n) for n = 0..165</a>
%H A169402 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).
%F A169402 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)/(6*t^32 - 3*t^31 - 3*t^30 - 3*t^29 - 3*t^28 - 3*t^27 - 3*t^26 - 3*t^25 - 3*t^24 - 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 - 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).
%F A169402 G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-3*sum(k=1..31,x^k)+6*x^32).
%o A169402 (PARI) x='x+O('x^66); /* that many terms */
%o A169402 Vec((1+2*sum(k=1,31,x^k)+x^32)/(1-3*sum(k=1,31,x^k)+6*x^32)) /* show terms */
%o A169402 /* _Joerg Arndt_, Jun 26 2011 */
%Y A169402 Cf. A003947 (G.f.: (1+x)/(1-4*x) ).
%K A169402 nonn
%O A169402 0,2
%A A169402 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009