login
A170720
Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
1
1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518976, 4462207721088, 169563893401344, 6443427949251072, 244850262071540736, 9304309958718547968, 353563778431304822784, 13435423580389583265792
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170758, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
About the initial comment, first disagreement is at index 50 and the difference is 741. - Vincenzo Librandi, Dec 06 2012
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, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).
FORMULA
G.f. (t^50 + 2*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)/(703*t^50 - 37*t^49 - 37*t^48 - 37*t^47 - 37*t^46 - 37*t^45 -
37*t^44 - 37*t^43 - 37*t^42 - 37*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)
MATHEMATICA
With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-37 t^Range[49]] + 703 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Vincenzo Librandi, Dec 06 2012 *)
coxG[{50, 703, -37}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 26 2018 *)
CROSSREFS
Sequence in context: A170576 A170624 A170672 * A170758 A218741 A112617
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved