|
|
A166165
|
|
Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
|
|
1
|
|
|
1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992186870, 99307704726518400, 3475769665427372880, 121651938289931061600, 4257817840146642534000, 149023624405099426920000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The initial terms coincide with those of A170755, 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 (34, 34, 34, 34, 34, 34, 34, 34, 34, -595).
|
|
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)/(595*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
|
|
MAPLE
|
seq(coeff(series((1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020
|
|
MATHEMATICA
|
CoefficientList[Series[(1+t)*(1-t^10)/(1-35*t+629*t^10-595*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)/(1-35*t+629*t^10-595*t^11) ).list()
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|