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A170639
Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
0
1, 6, 30, 150, 750, 3750, 18750, 93750, 468750, 2343750, 11718750, 58593750, 292968750, 1464843750, 7324218750, 36621093750, 183105468750, 915527343750, 4577636718750, 22888183593750, 114440917968750, 572204589843750
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003948, 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 (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).
FORMULA
G.f. (t^49 + 2*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)/(10*t^49 - 4*t^48 - 4*t^47 - 4*t^46 - 4*t^45 - 4*t^44 - 4*t^43 -
4*t^42 - 4*t^41 - 4*t^40 - 4*t^39 - 4*t^38 - 4*t^37 - 4*t^36 - 4*t^35 -
4*t^34 - 4*t^33 - 4*t^32 - 4*t^31 - 4*t^30 - 4*t^29 - 4*t^28 - 4*t^27 -
4*t^26 - 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20 - 4*t^19 -
4*t^18 - 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12 - 4*t^11 -
4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 -
4*t + 1)
CROSSREFS
Sequence in context: A170495 A170543 A170591 * A170687 A003948 A105488
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved