STATUS
proposed
approved
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Revision History for A166410
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
(history; published version)
(history; published version)
STATUS
editing
proposed
FORMULA
G.f.: (1+x)*(1-x^1211)/(1 - 15*x + 119*x^11 - 105*x^12). (End)
MATHEMATICA
With[{ap=105, bq=14}, CoefficientList[Series[(1+t)*(1-t^1211)/(1-(bq+1)*t + (ap+bq)*t^11-ap*t^12), {t, 0, 40}], t]] (* G. C. Greubel, May 12 2016; Jul 23 2024 *)
PROG
Coefficients(R!( (1+x)*(1-x^1211)/(1-15*x+119*x^11-105*x^12) )); // G. C. Greubel, Jul 23 2024
return P( (1+x)*(1-x^1211)/(1-15*x+119*x^11-105*x^12) ).list()
STATUS
proposed
editing
STATUS
editing
proposed
LINKS
<a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).
FORMULA
From G. C. Greubel, Jul 23 2024: (Start)
a(n) = 14*Sum_{j=1..10} a(n-j) - 105*a(n-11).
G.f.: (1+x)*(1-x^12)/(1 - 15*x + 119*x^11 - 105*x^12). (End)
MATHEMATICA
CoefficientList[Series[(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)/(105*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1), {t, 0, 500}], t] (* G. C. Greubel, May 12 2016 *)
With[{a=105, b=14}, CoefficientList[Series[(1+t)*(1-t^12)/(1-(b+1)*t + (a+b)*t^11-a*t^12), {t, 0, 40}], t]] (* G. C. Greubel, May 12 2016; Jul 23 2024 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^12)/(1-15*x+119*x^11-105*x^12) )); // G. C. Greubel, Jul 23 2024
(SageMath)
def A166410_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^12)/(1-15*x+119*x^11-105*x^12) ).list()
A166410_list(30) # G. C. Greubel, Jul 23 2024
STATUS
approved
editing
STATUS
editing
approved
MATHEMATICA
coxG[{11, 105, -14}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 24 2021 *)
STATUS
approved
editing
STATUS
editing
approved
LINKS
<a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).
STATUS
approved
editing
STATUS
reviewed
approved