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A169218
Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
0
1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144576, 804925734912, 9659108818944, 115909305827328, 1390911669927936, 16690940039135232, 200291280469622784
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170732, although the two sequences are eventually different.
First disagreement at index 28: a(28) = 1785817175576971922613630664626, A170732(28) = 1785817175576971922613630664704. - Klaus Brockhaus, May 24 2011
Computed with Magma using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).
FORMULA
G.f.: (t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*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)/(66*t^28 - 11*t^27 - 11*t^26 - 11*t^25 - 11*t^24 - 11*t^23 - 11*t^22 - 11*t^21 - 11*t^20 - 11*t^19 - 11*t^18 - 11*t^17 - 11*t^16 - 11*t^15 - 11*t^14 - 11*t^13 - 11*t^12 - 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).
MATHEMATICA
coxG[{28, 66, -11}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 11 2020 *)
CROSSREFS
Cf. A170732 (G.f.: (1+x)/(1-12*x)).
Sequence in context: A169074 A169122 A169170 * A169266 A169314 A169362
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved