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A163432
Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 12, 132, 1452, 15972, 175626, 1931160, 21234840, 233496120, 2567499000, 28231951770, 310435603500, 3413517587700, 37534684133100, 412727480315700, 4538308419052650, 49902767052699000, 548725632894681000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003954, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(55*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).
a(n) = 10*a(n-1)+10*a(n-2)+10*a(n-3)+10*a(n-4)-55*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-11*x+65*x^5-55*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{10, 10, 10, 10, -55}, {1, 12, 132, 1452, 15972, 175626}, 30] (* G. C. Greubel, Dec 23 2016 *)
coxG[{5, 55, -10}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-11*x+65*x^5-55*x^6)) \\ G. C. Greubel, Dec 23 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-11*x+65*x^5-55*x^6) )); // G. C. Greubel, May 12 2019
(Sage) ((1+x)*(1-x^5)/(1-11*x+65*x^5-55*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019
CROSSREFS
Sequence in context: A010580 A010577 A163055 * A163957 A063813 A164601
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved