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A170616
Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
0
1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610173000000000, 18305190000000000, 549155700000000000, 16474671000000000000, 494240130000000000000, 14827203900000000000000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170750, 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 (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).
FORMULA
G.f. (t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 +
2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*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)/(435*t^48 - 29*t^47 - 29*t^46 - 29*t^45 - 29*t^44 - 29*t^43 - 29*t^42
- 29*t^41 - 29*t^40 - 29*t^39 - 29*t^38 - 29*t^37 - 29*t^36 - 29*t^35 -
29*t^34 - 29*t^33 - 29*t^32 - 29*t^31 - 29*t^30 - 29*t^29 - 29*t^28 -
29*t^27 - 29*t^26 - 29*t^25 - 29*t^24 - 29*t^23 - 29*t^22 - 29*t^21 -
29*t^20 - 29*t^19 - 29*t^18 - 29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 -
29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 -
29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1)
CROSSREFS
Sequence in context: A170472 A170520 A170568 * A170664 A170712 A170750
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved