A170653 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964380, 44266298381323220, 841059669245141180, 15980133715657682420
Offset: 0
Keywords
Links
- Index entries for linear recurrences with constant coefficients, signature (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).
Programs
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Mathematica
With[{num=Total[2t^Range[ 0,49]]-1-t^49, den=Total[-18 t^Range[48]]+1+ 171t^49}, CoefficientList[ Series[num/den,{t,0,20}],t]] (* Harvey P. Dale, Jun 13 2011 *)
Formula
G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +
2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*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)/(171*t^49 - 18*t^48 - 18*t^47 - 18*t^46 - 18*t^45 - 18*t^44 - 18*t^43
- 18*t^42 - 18*t^41 - 18*t^40 - 18*t^39 - 18*t^38 - 18*t^37 - 18*t^36 -
18*t^35 - 18*t^34 - 18*t^33 - 18*t^32 - 18*t^31 - 18*t^30 - 18*t^29 -
18*t^28 - 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 - 18*t^23 - 18*t^22 -
18*t^21 - 18*t^20 - 18*t^19 - 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 -
18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 -
18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)
a(0)=1, a(1)=20, a(n)=19*a(n-1). - Harvey P. Dale, Jun 13 2011
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