cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A167092 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

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%I A167092 #11 Jun 21 2022 15:35:54
%S A167092 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A167092 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A167092 9304309958718547968,353563778431304822043,13435423580389583209476
%N A167092 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
%C A167092 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A167092 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167092 G. C. Greubel, <a href="/A167092/b167092.txt">Table of n, a(n) for n = 0..500</a>
%H A167092 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).
%F A167092 G.f.: (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)/(703*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).
%t A167092 CoefficientList[Series[(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)/(703*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 02 2016 *)
%t A167092 coxG[{13,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 21 2022 *)
%K A167092 nonn
%O A167092 0,2
%A A167092 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009