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A167980 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I. 7
1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170767, 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 (46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,-1081).
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)/( 1081*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
From G. C. Greubel, Jan 17 2023: (Start)
a(n) = Sum_{j=1..15} a(n-j) - 1081*a(n-16).
G.f.: (1+x)*(1-x^17)/(1 - 47*x + 1127*x^16 - 1081*x^17). (End)
MATHEMATICA
coxG[{16, 1081, -46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 12 2016 *)
CoefficientList[Series[(1+t)*(1-t^17)/(1-47*t+1127*t^16-1081*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 03 2016; Jan 17 2023 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^17)/(1-47*x+1127*x^16-1081*x^17) )); // G. C. Greubel, Jan 17 2023
(SageMath)
def A167980_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^17)/(1-47*x+1127*x^16-1081*x^17) ).list()
A167980_list(30) # G. C. Greubel, Jan 17 2023
CROSSREFS
Sequence in context: A167101 A167645 A167863 * A168725 A168773 A168821
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)