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A166324
Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569138536, 3181328043318593280, 152703746079289769112, 7329779811805778917632, 351829430966671148058624
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170768, 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 (47,47,47,47,47,47,47,47,47,-1128).
FORMULA
G.f.: (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)/(1128*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-48*t+1175*t^10-1128*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 12 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-48*t+1175*t^10-1128*t^11), {t, 0, 30}], t] (* _G, C, Greubel_, May 09 2016 *)
coxG[{10, 1128, -47}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 12 2020 *)
PROG
(Sage)
def A166324_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-48*t+1175*t^10-1128*t^11) ).list()
A166324_list(30) # G. C. Greubel, Mar 12 2020
CROSSREFS
Sequence in context: A164694 A165181 A165709 * A166443 A166855 A167102
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved