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A163564
Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 31, 930, 27900, 837000, 25109535, 753272100, 22597744965, 677919807900, 20337218005500, 610105253435760, 18302819007466125, 549074412543683490, 16471927651538698875, 494148687972122850750, 14824186397015923722360
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170750, 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)/(435*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).
a(n) = 29*a(n-1)+29*a(n-2)+29*a(n-3)+29*a(n-4)-435*a(n-5). - Wesley Ivan Hurt, May 11 2021
MATHEMATICA
With[{num=Total[2t^Range[4]]+t^5+1, den=Total[-29 t^Range[4]]+435t^5+1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Sep 16 2011 *)
CoefficientList[Series[(1+x)*(1-x^5)/(1-30*x+464*x^5-435*x^6), {x, 0, 20}], x] (* or *) coxG[{5, 435, -29}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 18 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-30*x+464*x^5-435*x^6)) \\ G. C. Greubel, Jul 28 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-30*x+464*x^5-435*x^6) )); // G. C. Greubel, May 18 2019
(Sage) ((1+x)*(1-x^5)/(1-30*x+464*x^5-435*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 18 2019
CROSSREFS
Sequence in context: A157878 A162835 A163214 * A164030 A164667 A164992
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved