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A162987
Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
2
1, 11, 110, 1100, 10945, 108900, 1083555, 10781100, 107269470, 1067306625, 10619454780, 105661128375, 1051303881870, 10460231387100, 104076892111005, 1035541095642900, 10303395297584895, 102516409155629700, 1020014649794722230, 10148910738927500925
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003953, 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)/(45*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
From G. C. Greubel, Apr 28 2019: (Start)
a(n) = 9*(a(n-1) + a(n-2) + a(n-3) - 5*a(n-4)).
G.f.: (1+x)*(1-x^4)/(1 - 10*x + 54*x^4 - 45*x^5). (End)
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5), {x, 0, 20}], x] (* or *) coxG[{4, 45, -9}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5)) \\ G. C. Greubel, Apr 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[11, 110, 1100, 10945];; for n in [5..20] do a[n]:=9*(a[n-1]+a[n-2] +a[n-3] -5*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019
CROSSREFS
Sequence in context: A352574 A121031 A115804 * A163404 A115808 A163955
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved