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A164113
Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 43, 1806, 75852, 3185784, 133802928, 5619722073, 236028289140, 9913186551891, 416353768315884, 17486855460998532, 734447811414657312, 30846803125630618266, 1295565523217549867745, 54413743236663181589148
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170762, 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)/(861*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).
a(n) = -861*a(n-6) + 41*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-42*t+902*t^6-861*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 16 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-42*t+902*t^6-861*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 11 2017 *)
coxG[{6, 861, -41}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 16 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-42*t+902*t^6-861*t^7)) \\ G. C. Greubel, Sep 11 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-42*t+902*t^6-861*t^7) )); // G. C. Greubel, Aug 10 2019
(Sage)
def A164113_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-42*t+902*t^6-861*t^7)).list()
A164113_list(30) # G. C. Greubel, Aug 10 2019
(GAP) a:=[43, 1806, 75852, 3185784, 133802928, 5619722073];; for n in [7..30] do a[n]:=41*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -861*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019
CROSSREFS
Sequence in context: A162881 A163226 A163745 * A164687 A165175 A165694
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved