login
A166129
Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 33, 1056, 33792, 1081344, 34603008, 1107296256, 35433480192, 1133871366144, 36283883716608, 1161084278930928, 37154696925772800, 1188950301624189456, 38046409651956777984, 1217485108862063788032, 38959523483568341778432
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170752, 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 (31, 31, 31, 31, 31, 31, 31, 31, 31, -496).
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)/(496*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-32*t+527*t^10-496*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Mar 11 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1 -32*t +527*t^10 -496*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 26 2016 *)
coxG[{496, 10, -31}] (* The coxG program is at A169452 *) (* G. C. Greubel, Mar 11 2020 *)
PROG
(Sage)
def A166129_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-32*t+527*t^10-496*t^11) ).list()
A166129_list(30) # G. C. Greubel, Mar 11 2020
CROSSREFS
Sequence in context: A164669 A165140 A165645 * A166427 A166679 A167086
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved