login
A166412
Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
1
1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890207929, 616894133532192, 10487200270003200, 178282404589305312, 3030800878005455808, 51523614925876262304
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170737, 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 (16,16,16,16,16,16,16,16,16,16,-136).
FORMULA
G.f.: (t^11 + 2*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)/(136*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
From G. C. Greubel, Jul 23 2024: (Start)
a(n) = 16*Sum_{j=1..10} a(n-j) - 136*a(n-11).
G.f.: (1+x)*(1 - x^11)/(1 - 17*x + 152*x^11 - 136*x^12). (End)
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^11)/(1-17*t+152*t^11-136*t^12), {t, 0, 50}], t] (* G. C. Greubel, May 12 2016; Jul 23 2024 *)
coxG[{11, 136, -16, 30}] (* The coxG program is at A169452 *)(* G. C. Greubel, Jul 23 2024 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-17*x+152*x^11-136*x^12) )); // G. C. Greubel, Jul 23 2024
(SageMath)
def A166412_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^11)/(1-17*x+152*x^11-136*x^12) ).list()
A166412_list(30) # G. C. Greubel, Jul 23 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved