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A164049
Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 33, 1056, 33792, 1081344, 34603008, 1107295728, 35433446400, 1133869744656, 36283814544384, 1161081512312832, 37154590694572032, 1188946335844548336, 38046264622817975040, 1217479887955809181968, 38959337855415022281984
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.
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(496*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).
a(n) = -496*a(n-6) + 31*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-32*t+527*t^6-496*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-32*t+527*t^6-496*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 08 2017 *)
coxG[{6, 496, -31}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 13 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-32*t+527*t^6-496*t^7)) \\ G. C. Greubel, Sep 08 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-32*t+527*t^6-496*t^7) )); // G. C. Greubel, Aug 13 2019
(Sage)
def A164049_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-32*t+527*t^6-496*t^7)).list()
A164049_list(30) # G. C. Greubel, Aug 13 2019
(GAP) a:=[33, 1056, 33792, 1081344, 34603008, 1107295728];; for n in [7..30] do a[n]:=31*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -496*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019
CROSSREFS
Sequence in context: A324951 A163216 A163567 * A164669 A165140 A165645
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved