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A168853
Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
0
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.
First disagreement at index 20: a(20) = 693461191039052678230856878576, A170751(20) = 693461191039052678230856879072. - 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 (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
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)/(465*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
coxG[{20, 465, -30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 03 2022 *)
CROSSREFS
Cf. A170751 (G.f.: (1+x)/(1-31*x)).
Sequence in context: A168709 A168757 A168805 * A168901 A168949 A168997
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved