login
A164601
Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
1
1, 12, 132, 1452, 15972, 175692, 1932612, 21258666, 233844600, 2572282680, 28295022360, 311244287640, 3423676622520, 37660326891000, 414262320281370, 4556871492422700, 50125432079728500, 551378055176107500
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003954, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(55*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).
a(n) = -55*a(n-7) + 10*Sum_{k=1..6} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 28 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8), {t, 0, 30}], t] (* G. C. Greubel, Aug 11 2017 *)
coxG[{7, 55, -10}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 28 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8)) \\ G. C. Greubel, Aug 11 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8) )); // G. C. Greubel, Aug 28 2019
(Sage)
def A164601_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8)).list()
A164601_list(30) # G. C. Greubel, Aug 28 2019
(GAP) a:=[12, 132, 1452, 15972, 175692, 1932612, 21258666];; for n in [8..30] do a[n]:=10*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -55*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Aug 28 2019
CROSSREFS
Sequence in context: A163432 A163957 A063813 * A164781 A165266 A165807
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved