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A170594
Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
0
1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959552, 9663676416, 77309411328, 618475290624, 4947802324992, 39582418599936, 316659348799488, 2533274790395904, 20266198323167232, 162129586585337856
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003951, 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 (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -28).
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)/(28*t^48 - 7*t^47 - 7*t^46 - 7*t^45 - 7*t^44 - 7*t^43 - 7*t^42 -
7*t^41 - 7*t^40 - 7*t^39 - 7*t^38 - 7*t^37 - 7*t^36 - 7*t^35 - 7*t^34 -
7*t^33 - 7*t^32 - 7*t^31 - 7*t^30 - 7*t^29 - 7*t^28 - 7*t^27 - 7*t^26 -
7*t^25 - 7*t^24 - 7*t^23 - 7*t^22 - 7*t^21 - 7*t^20 - 7*t^19 - 7*t^18 -
7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 -
7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1)
MATHEMATICA
With[{num=Total[2t^Range[47]]+t^48+1, den=Total[-7 t^Range[47]]+28t^48+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Apr 07 2013 *)
CROSSREFS
Sequence in context: A170450 A170498 A170546 * A170642 A170690 A003951
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved