|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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 *)
|
|
PROG
|
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-38*t+740*t^10-703*t^11) ).list()
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|