login
A163316
Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 5, 20, 80, 320, 1270, 5040, 20010, 79440, 315360, 1251930, 4969980, 19730070, 78325380, 310939920, 1234384470, 4900319640, 19453527810, 77227563240, 306581745960, 1217083163130, 4831636082580, 19180864497870, 76145131089180
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003947, 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)/(6*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).
a(n) = 3*a(n-1)+3*a(n-2)+3*a(n-3)+3*a(n-4)-6*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-4*x+9*x^5-6*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, 3, 3, 3, -6}, {1, 5, 20, 80, 320, 1270}, 30] (* G. C. Greubel, Dec 18 2016 *)
coxG[{5, 6, -3}] (* 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)/(1-4*x+9*x^5-6*x^6)) \\ G. C. Greubel, Dec 18 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-4*x+9*x^5-6*x^6) )); // G. C. Greubel, May 12 2019
(Sage) ((1+x)*(1-x^5)/(1-4*x+9*x^5-6*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019
CROSSREFS
Sequence in context: A154639 A214939 A162925 * A163878 A164354 A164706
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved