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A166171
Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518976, 4462207721088, 169563893401344, 6443427949250331, 244850262071484420, 9304309958715338697, 353563778431142238492, 13435423580381861046924
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170758, 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 (37, 37, 37, 37, 37, 37, 37, 37, 37, -703).
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)/(703*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-38*t+740*t^10-703*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-38*t+740*t^10-703*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 06 2016 *)
coxG[{703, 10, -37}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)
PROG
(Sage)
def A166171_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-38*t+740*t^10-703*t^11) ).list()
A166171_list(30) # G. C. Greubel, Aug 10 2019
CROSSREFS
Sequence in context: A164681 A165171 A165688 * A166433 A166691 A167092
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved