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A170729
Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
1
1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170767, 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 1128. - Vincenzo Librandi, Dec 08 2012
LINKS
Index entries for linear recurrences with constant coefficients, signature (46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, -1080).
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)/(1081*t^50 - 46*t^49 - 46*t^48 - 46*t^47 - 46*t^46 - 46*t^45 -
46*t^44 - 46*t^43 - 46*t^42 - 46*t^41 - 46*t^40 - 46*t^39 - 46*t^38 -
46*t^37 - 46*t^36 - 46*t^35 - 46*t^34 - 46*t^33 - 46*t^32 - 46*t^31 -
46*t^30 - 46*t^29 - 46*t^28 - 46*t^27 - 46*t^26 - 46*t^25 - 46*t^24 -
46*t^23 - 46*t^22 - 46*t^21 - 46*t^20 - 46*t^19 - 46*t^18 - 46*t^17 -
46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 -
46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 -
46*t + 1)
MATHEMATICA
With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-46 t^Range[49]] + 1081 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Vincenzo Librandi, Dec 08 2012 *)
coxG[{50, 1081, -46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 07 2024 *)
CROSSREFS
Sequence in context: A170585 A170633 A170681 * A063822 A170767 A218750
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved