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A168866
Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
0
1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501434880, 632170063134720, 27815482777927680, 1223881242228817920, 53850774658067988480, 2369434084954991493120, 104255099738019625697280
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170764, although the two sequences are eventually different.
First disagreement at index 20: a(20) = 756507724787653779947106525510690, A170764(20) = 756507724787653779947106525511680. - Klaus Brockhaus, Apr 04 2011
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
FORMULA
G.f.: (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)/(946*t^20 - 43*t^19 - 43*t^18 - 43*t^17 - 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
MATHEMATICA
coxG[{20, 946, -43}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 17 2020 *)
CROSSREFS
Cf. A170764 (G.f.: (1+x)/(1-44*x)).
Sequence in context: A168722 A168770 A168818 * A168914 A168962 A169010
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved