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A163518 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
1, 23, 506, 11132, 244904, 5387635, 118522404, 2607370689, 57359466780, 1261849124844, 27759379635372, 610677728876061, 13434280356535038, 295540315560771435, 6501582206394337062, 143028104664155140584 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170742, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
FORMULA
G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).
a(n) = 21*a(n-1)+21*a(n-2)+21*a(n-3)+21*a(n-4)-231*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 231, -21}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 16 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6)) \\ G. C. Greubel, Jul 27 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019
CROSSREFS
Sequence in context: A162809 A212336 A163171 * A163991 A164636 A164957
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved

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Last modified April 21 10:46 EDT 2024. Contains 371852 sequences. (Running on oeis4.)