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A163232
Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
1
1, 46, 2070, 93150, 4190715, 188535600, 8482007160, 381596054400, 17167581467190, 772350369021000, 34747182860785560, 1563237055602189000, 70328294002955286540, 3163991615757072698400, 142344458748855549948960
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170765, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(990*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).
a(n) = 44*a(n-1)+44*a(n-2)+44*a(n-3)-990*a(n-4). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(990*t^4-44*t^3-44*t^2 - 44*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[ {44, 44, 44, -990}, {46, 2070, 93150, 4190715}, 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 990, -44}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 01 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(990*t^4-44*t^3 - 44*t^2-44*t+1)) \\ G. C. Greubel, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^4)/(1-45*x+1034*x^4-990*x^5) )); // G. C. Greubel, May 01 2019
(Sage) ((1+x)*(1-x^4)/(1-45*x+1034*x^4-990*x^5)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019
(GAP) a:=[46, 2070, 93150, 4190715];; for n in [5..20] do a[n]:=44*(a[n-1] +a[n-2] +a[n-3]) -990*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, May 01 2019
CROSSREFS
Sequence in context: A223813 A324451 A162889 * A163802 A164331 A164691
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved