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A162881
Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
1
1, 43, 1806, 74949, 3109932, 129025155, 5353007478, 222085686501, 9213895794684, 382266301290027, 15859472304395790, 657978118553895573, 27298209939779232636, 1132548704737573481379, 46987204341696557186262
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^3 + 2*t^2 + 2*t + 1)/(861*t^3 - 41*t^2 - 41*t + 1).
a(n) = 41*a(n-1) + 41*a(n-2) - 861*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018
G.f.: (1+x)*(1-x^3)/(1 -42*x + 902*x^3 - 861*x^4). - G. C. Greubel, Apr 27 2019
MAPLE
seq(coeff(series((x^3+2*x^2+2*x+1)/(861*x^3-41*x^2-41*x+1), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 24 2018
MATHEMATICA
CoefficientList[Series[(t^3+2*t^2+2*t+1)/(861*t^3-41*t^2-41*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)
coxG[{3, 861, -41}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 27 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(861*t^3-41*t^2-41*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(861*t^3-41*t^2-41*t+1))); // G. C. Greubel, Oct 24 2018
(GAP) a:=[43, 1806, 74949];; for n in [4..20] do a[n]:=41*a[n-1]+41*a[n-2] -861*a[n-3]; od; Concatenation([1], a); # Muniru A Asiru, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1 -42*x +902*x^3 -861*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 27 2019
CROSSREFS
Sequence in context: A022220 A297028 A198206 * A163226 A163745 A164113
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved