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A163519
Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 24, 552, 12696, 292008, 6715908, 154459536, 3552423600, 81702391056, 1879077904176, 43217018799372, 993950655137880, 22859927229943848, 525756756894338904, 12091909332851083560, 278102505382114851108
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170743, 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)/(253*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).
a(n) = 22*a(n-1)+22*a(n-2)+22*a(n-3)+22*a(n-4)-253*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 253, -22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 16 2018 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6)) \\ G. C. Greubel, Jul 27 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019
CROSSREFS
Sequence in context: A334673 A342888 A163174 * A163992 A164637 A164959
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved