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A167225
Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.
1
1, 26, 650, 16250, 406250, 10156250, 253906250, 6347656250, 158691406250, 3967285156250, 99182128906250, 2479553222656250, 61988830566406250, 1549720764160156250, 38743019104003905925, 968575477600097640000
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OFFSET
0,2
COMMENTS
The initial terms coincide with those of
A170745
, although the two sequences are eventually different.
Computed with Magma using commands similar to those used to compute
A154638
.
LINKS
G. C. Greubel,
Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients
, signature (24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, -300).
FORMULA
G.f.: (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)/(300*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).
MATHEMATICA
CoefficientList[Series[(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)/ (300*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1), {t, 0, 50}], t] (*
G. C. Greubel
, Jun 05 2016 *)
coxG[{14, 300, -24}] (* The coxG program is at
A169452
*) (*
Harvey P. Dale
, Sep 16 2018 *)
CROSSREFS
Sequence in context:
A166420
A166613
A167079
*
A167697
A167941
A168703
Adjacent sequences:
A167222
A167223
A167224
*
A167226
A167227
A167228
KEYWORD
nonn
AUTHOR
John Cannon
and
N. J. A. Sloane
, Dec 03 2009
STATUS
approved