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A170537 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

%I A170537 #8 Sep 26 2024 18:07:26
%S A170537 1,48,2256,106032,4983504,234224688,11008560336,517402335792,
%T A170537 24317909782224,1142941759764528,53718262708932816,
%U A170537 2524758347319842352,118663642324032590544,5577191189229531755568,262127985893787992511696
%N A170537 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
%C A170537 The initial terms coincide with those of A170767, although the two sequences are eventually different.
%C A170537 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170537 <a href="/index/Rec#order_46">Index entries for linear recurrences with constant coefficients</a>, signature (46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, -1081).
%F A170537 G.f. (t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 +
%F A170537 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170537 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170537 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170537 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170537 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^46 - 46*t^45 -
%F A170537 46*t^44 - 46*t^43 - 46*t^42 - 46*t^41 - 46*t^40 - 46*t^39 - 46*t^38 -
%F A170537 46*t^37 - 46*t^36 - 46*t^35 - 46*t^34 - 46*t^33 - 46*t^32 - 46*t^31 -
%F A170537 46*t^30 - 46*t^29 - 46*t^28 - 46*t^27 - 46*t^26 - 46*t^25 - 46*t^24 -
%F A170537 46*t^23 - 46*t^22 - 46*t^21 - 46*t^20 - 46*t^19 - 46*t^18 - 46*t^17 -
%F A170537 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 -
%F A170537 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 -
%F A170537 46*t + 1)
%t A170537 coxG[{46,1081,-46}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 26 2024 *)
%K A170537 nonn
%O A170537 0,2
%A A170537 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009