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A167988
Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
7
1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297896448, 7329779811806299029504, 351829430966702353416192
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170768, although the two sequences are eventually different.
Computed with Magma using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,-1128).
FORMULA
G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/( 1128*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
From G. C. Greubel, Jan 14 2023: (Start)
a(n) = -1128*a(n-16) + 47*Sum_{j=1..15} a(n-j).
G.f.: (1 + x)*(1 - x^16)/(1 - 48*x + 1175*x^16 - 1128*x^17). (End)
MATHEMATICA
coxG[{16, 1128, -47}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 05 2015 *)
CoefficientList[Series[(1+x)*(1-x^16)/(1-48*x+1175*x^16-1128*x^17), {x, 0, 50}], x] (* G. C. Greubel, Jul 03 2016; Jan 14 2023 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-48*x+1175*x^16-1128*x^17) )); // G. C. Greubel, Jan 14 2023
(Sage)
def A167988_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^16)/(1-48*x+1175*x^16-1128*x^17) ).list()
A167988_list(40) # G. C. Greubel, Jan 14 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved