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A164697 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I. 1
1, 4, 12, 36, 108, 324, 972, 2916, 8742, 26208, 78576, 235584, 706320, 2117664, 6349104, 19035648, 57071982, 171111132, 513019140, 1538115228, 4611520836, 13826093148, 41452886916, 124282529820, 372619336494, 1117173669768 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003946, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
FORMULA
G.f.: (x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1)/( 3*x^8 - 2*x^7 - 2*x^6 - 2*x^5 - 2*x^4 - 2*x^3 - 2*x^2 - 2*x + 1).
a(n) = -3*a(n-8) + 2*Sum_{k=1..7} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^8)/(1-3*t+5*t^8-3*t^9), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 16 2019
MATHEMATICA
CoefficientList[Series[(x^8 +2x^7 +2x^6 +2x^5 +2x^4 +2x^3 +2x^2 +2x +1)/( 3x^8 -2x^7 -2x^6 -2x^5 -2x^4 -2x^3 -2x^2 -2x +1), {x, 0, 40}], x ] (* Vincenzo Librandi, Apr 29 2014 *)
coxG[{8, 3, -2, 30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 03 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^8)/(1-3*t+5*t^8-3*t^9)) \\ G. C. Greubel, Sep 16 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^8)/(1-3*t+5*t^8-3*t^9) )); // G. C. Greubel, Sep 16 2019
(Sage)
def A164697_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^8)/(1-3*t+5*t^8-3*t^9)).list()
A164697_list(30) # G. C. Greubel, Sep 16 2019
(GAP) a:=[4, 12, 36, 108, 324, 972, 2916, 8742];; for n in [9..30] do a[n]:=2*Sum([1..7], j-> a[n-j]) -3*a[n-8]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019
CROSSREFS
Sequence in context: A336262 A164353 A347506 * A165184 A165756 A166328
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved

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Last modified April 19 05:19 EDT 2024. Contains 371782 sequences. (Running on oeis4.)