login
A167949
Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
7
1, 33, 1056, 33792, 1081344, 34603008, 1107296256, 35433480192, 1133871366144, 36283883716608, 1161084278931456, 37154696925806592, 1188950301625810944, 38046409652025950208, 1217485108864830406656, 38959523483674573012992
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170752, 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 (31,31,31,31,31,31,31,31,31,31,31,31,31,31,31,-496).
FORMULA
G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*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)/( 496*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).
From G. C. Greubel, Sep 07 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 32*t + 527*t^16 - 496*t^17).
a(n) = 31*Sum_{j=1..15} a(n-j) - 496*a(n-16). (End)
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^16)/(1-32*t+527*t^16-496*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 02 2016; Sep 07 2023 *)
coxG[{16, 496, -31}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 22 2020 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-32*x+527*x^16-496*x^17) )); // G. C. Greubel, Sep 07 2023
(SageMath)
def A167949_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^16)/(1-32*x+527*x^16-496*x^17) ).list()
A167949_list(40) # G. C. Greubel, Sep 07 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved