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.

A167095 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

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%I A167095 #11 Nov 24 2016 10:35:35
%S A167095 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A167095 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A167095 23113819332082434522,947666592615379814541,38854330297230572360880
%N A167095 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
%C A167095 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A167095 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167095 G. C. Greubel, <a href="/A167095/b167095.txt">Table of n, a(n) for n = 0..500</a>
%H A167095 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).
%F A167095 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)/(820*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1).
%t A167095 coxG[{13,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 21 2014 *)
%t A167095 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)/(820*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 02 2016 *)
%K A167095 nonn
%O A167095 0,2
%A A167095 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009