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A170631
Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
0
1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558593750, 1566328930136718750, 70484801856152343750, 3171816083526855468750, 142731723758708496093750
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170765, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, -990).
FORMULA
G.f. (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)/(990*t^48 - 44*t^47 - 44*t^46 - 44*t^45 - 44*t^44 - 44*t^43 - 44*t^42
- 44*t^41 - 44*t^40 - 44*t^39 - 44*t^38 - 44*t^37 - 44*t^36 - 44*t^35 -
44*t^34 - 44*t^33 - 44*t^32 - 44*t^31 - 44*t^30 - 44*t^29 - 44*t^28 -
44*t^27 - 44*t^26 - 44*t^25 - 44*t^24 - 44*t^23 - 44*t^22 - 44*t^21 -
44*t^20 - 44*t^19 - 44*t^18 - 44*t^17 - 44*t^16 - 44*t^15 - 44*t^14 -
44*t^13 - 44*t^12 - 44*t^11 - 44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 -
44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1)
MATHEMATICA
coxG[{48, 990, -44}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 22 2019 *)
CROSSREFS
Sequence in context: A170487 A170535 A170583 * A170679 A170727 A170765
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved