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A170492
Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
0
1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003945, 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 (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1).
FORMULA
G.f. (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)/(t^46 - t^45 - t^44 -
t^43 - t^42 - t^41 - t^40 - t^39 - t^38 - t^37 - t^36 - t^35 - t^34 -
t^33 - t^32 - t^31 - t^30 - t^29 - t^28 - t^27 - t^26 - t^25 - t^24 -
t^23 - t^22 - t^21 - t^20 - t^19 - t^18 - t^17 - t^16 - t^15 - t^14 -
t^13 - t^12 - t^11 - t^10 - t^9 - t^8 - t^7 - t^6 - t^5 - t^4 - t^3 -
t^2 - t + 1)
MATHEMATICA
With[{num=Total[2t^Range[45]]+t^46+1, den=Total[-t^Range[45]]+t^46+1}, CoefficientList[ Series[ num/den, {t, 0, 40}], t]] (* Harvey P. Dale, Jan 16 2012 *)
CROSSREFS
Sequence in context: A170348 A170396 A170444 * A170540 A170588 A170636
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved