A167048 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135545, 178282404592301664, 3030800878069084224, 51523614927173682720
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..500
- Index entries for linear recurrences with constant coefficients, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
Programs
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Magma
R
:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^13)/(1-17*x+152*x^13-136*x^14) )); // G. C. Greubel, Apr 26 2019 -
Mathematica
CoefficientList[Series[(1+x)*(1-x^13)/(1-17*x+152*x^13-136*x^14), {x, 0, 20}], x] (* G. C. Greubel, May 30 2016, modified Apr 26 2019 *) coxG[{13, 136, -16}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *) -
PARI
my(x='x+O('x^20)); Vec((1+x)*(1-x^13)/(1-17*x+152*x^13-136*x^14)) \\ G. C. Greubel, Apr 26 2019 -
Sage
((1+x)*(1-x^13)/(1-17*x+152*x^13-136*x^14)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019
Formula
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)/(136*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
G.f.: (1+x)*(1-x^13)/(1 - 17*x + 152*x^13 - 136*x^14). - G. C. Greubel, Apr 26 2019
a(n) = -136*a(n-13) + 16*Sum_{k=1..12} a(n-k). - Wesley Ivan Hurt, May 06 2021
Comments