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A166419
Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
1
1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134100, 38042028579211200, 913008685900896300, 21912208461617371200, 525893003078717548800
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170744, 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 (23,23,23,23,23,23,23,23,23,23,-276).
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)/(276*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).
From G. C. Greubel, Jul 23 2024: (Start)
a(n) = 23*Sum_{j=1..10} a(n-j) - 276*a(n-11).
G.f.: (1+x)*(1-x^11)/(1 - 24*x + 299*x^11 - 276*x^12). (End)
MATHEMATICA
With[{p=276, q=23}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(q+1)*t + (p+q)*t^11-p*t^12), {t, 0, 40}], t]] (* G. C. Greubel, May 13 2016; Jul 23 2024 *)
coxG[{11, 276, -23, 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)/(1-24*x+299*x^11-276*x^12) )); // G. C. Greubel, Jul 23 2024
(SageMath)
def A166419_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^11)/(1-24*x+299*x^11-276*x^12) ).list()
A166419_list(30) # G. C. Greubel, Jul 23 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved