A170288 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518976, 4462207721088, 169563893401344, 6443427949251072, 244850262071540736, 9304309958718547968, 353563778431304822784, 13435423580389583265792
Offset: 0
Keywords
Links
- Index entries for linear recurrences with constant coefficients, signature (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).
Programs
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Mathematica
coxG[{41,703,-37}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 12 2022 *)
Formula
G.f. (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)/(703*t^41 - 37*t^40 - 37*t^39 - 37*t^38 - 37*t^37 - 37*t^36 - 37*t^35
- 37*t^34 - 37*t^33 - 37*t^32 - 37*t^31 - 37*t^30 - 37*t^29 - 37*t^28 -
37*t^27 - 37*t^26 - 37*t^25 - 37*t^24 - 37*t^23 - 37*t^22 - 37*t^21 -
37*t^20 - 37*t^19 - 37*t^18 - 37*t^17 - 37*t^16 - 37*t^15 - 37*t^14 -
37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 -
37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1)
Comments