login
A163660
Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 38, 1406, 52022, 1924814, 71217415, 2635018344, 97494717024, 3607268946840, 133467634460304, 4938253762332042, 182713586854206456, 6760336027236505128, 250129965636431546040, 9254717436709694665512
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170757, 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)/(666*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).
a(n) = 36*a(n-1)+36*a(n-2)+36*a(n-3)+36*a(n-4)-666*a(n-5). - Wesley Ivan Hurt, May 11 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 01 2017 *)
coxG[{5, 666, -36}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 22 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6)) \\ G. C. Greubel, Aug 01 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[38, 1406, 52022, 1924814, 71217415];; for n in [6..20] do a[n]:=36*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) - 666*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019
CROSSREFS
Sequence in context: A268885 A162858 A163221 * A164071 A164674 A165170
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved