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A165980
Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579258, 5764951698629760, 155653695862728336, 4202649788286235104, 113471544283527738672, 3063731695649832497472
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170747, 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 (26,26,26,26,26,26,26,26,26,-351).
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)/(351*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Oct 25 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 20 2016 *)
coxG[{10, 351, -26}] (* The coxG program is at A169452 *) (* G. C. Greubel, Oct 25 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11)) \\ G. C. Greubel, Oct 25 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11) )); // G. C. Greubel, Oct 25 2019
(Sage)
def A165980_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11)).list()
A165980_list(30) # G. C. Greubel, Oct 25 2019
(GAP) a:=[28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579258];; for n in [11..30] do a[n]:=26*Sum([1..9], j-> a[n-j]) - 351*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Oct 25 2019
CROSSREFS
Sequence in context: A164664 A164970 A165456 * A166422 A166615 A167081
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved