A169546 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520, 83886080, 335544320, 1342177280, 5368709120, 21474836480, 85899345920, 343597383680, 1374389534720, 5497558138880, 21990232555520, 87960930222080
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).
Programs
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Magma
R
:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (1+x)*(1-x^35)/(1-4*x+9*x^35-6*x^36) )); // G. C. Greubel, Apr 25 2019 -
Mathematica
coxG[{35,6,-3,30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 16 2015 *) CoefficientList[Series[(1+x)*(1-x^35)/(1-4*x+9*x^35-6*x^36), {x, 0, 25}], x] (* G. C. Greubel, Apr 25 2019 *) -
PARI
my(x='x+O('x^25)); Vec((1+x)*(1-x^35)/(1-4*x+9*x^35-6*x^36)) \\ G. C. Greubel, Apr 25 2019 -
Sage
((1+x)*(1-x^35)/(1-4*x+9*x^35-6*x^36)).series(x, 25).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
Formula
G.f.: (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*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)/(6*t^35 - 3*t^34 - 3*t^33 - 3*t^32 - 3*t^31 - 3*t^30 - 3*t^29 - 3*t^28 - 3*t^27 - 3*t^26 - 3*t^25 - 3*t^24 - 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 - 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).
G.f.: (1+x)*(1-x^35)/(1 - 4*x + 9*x^35 - 6*x^36). - G. C. Greubel, Apr 25 2019
Comments