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.

A167091 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

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%I A167091 #12 Nov 24 2016 10:34:27
%S A167091 1,38,1406,52022,1924814,71218118,2635070366,97497603542,
%T A167091 3607411331054,133474219248998,4938546112212926,182726206151878262,
%U A167091 6760869627619495694,250152176221921339975,9255630520211089553064
%N A167091 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
%C A167091 The initial terms coincide with those of A170757, although the two sequences are eventually different.
%C A167091 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167091 G. C. Greubel, <a href="/A167091/b167091.txt">Table of n, a(n) for n = 0..500</a>
%H A167091 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, -666).
%F A167091 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)/(666*t^13 - 36*t^12 - 36*t^11 - 36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).
%t A167091 coxG[{13,666,-36}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 13 2015 *)
%t A167091 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)/(666*t^13 - 36*t^12 - 36*t^11 - 36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 01 2016 *)
%K A167091 nonn
%O A167091 0,2
%A A167091 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009