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A169190
Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
1
1, 33, 1056, 33792, 1081344, 34603008, 1107296256, 35433480192, 1133871366144, 36283883716608, 1161084278931456, 37154696925806592, 1188950301625810944, 38046409652025950208, 1217485108864830406656, 38959523483674573012992
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170752, although the two sequences are eventually different.
First disagreement at index 27: a(27) = 44917272433563877177165448180993403911664, A170752(27) = 44917272433563877177165448180993403912192. - Klaus Brockhaus, May 07 2011
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, -496).
FORMULA
G.f.: (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)/(496*t^27 - 31*t^26 - 31*t^25 - 31*t^24 - 31*t^23 - 31*t^22 - 31*t^21 - 31*t^20 - 31*t^19 - 31*t^18 - 31*t^17 - 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).
MATHEMATICA
coxG[{27, 496, -31}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 07 2024 *)
CROSSREFS
Cf. A170752 (G.f.: (1+x)/(1-32*x)).
Sequence in context: A169046 A169094 A169142 * A169238 A169286 A169334
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved