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A170713
Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
1
1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170751, 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 496. - Vincenzo Librandi, Dec 06 2012
LINKS
Index entries for linear recurrences with constant coefficients, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
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)/(465*t^50 - 30*t^49 - 30*t^48 - 30*t^47 - 30*t^46 - 30*t^45 -
30*t^44 - 30*t^43 - 30*t^42 - 30*t^41 - 30*t^40 - 30*t^39 - 30*t^38 -
30*t^37 - 30*t^36 - 30*t^35 - 30*t^34 - 30*t^33 - 30*t^32 - 30*t^31 -
30*t^30 - 30*t^29 - 30*t^28 - 30*t^27 - 30*t^26 - 30*t^25 - 30*t^24 -
30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 - 30*t^19 - 30*t^18 - 30*t^17 -
30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 -
30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 -
30*t + 1).
MATHEMATICA
With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-30 t^Range[49]] + 465 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Vincenzo Librandi, Dec 06 2012 *)
coxG[{50, 465, -30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 15 2018 *)
CROSSREFS
Sequence in context: A170569 A170617 A170665 * A170751 A218734 A065552
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved