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A168728
Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
1
1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393213, 786420, 1572831, 3145644, 6291252, 12582432, 25164720, 50329152, 100657728, 201314304, 402626304, 805248000, 1610486784, 3220955136
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003945, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 393213, A003945(18) = 393216. - Klaus Brockhaus, Mar 27 2011
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).
FORMULA
G.f.: (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^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
CoefficientList[Series[(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^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), {t, 0, 50}], t] (* G. C. Greubel, Aug 06 2016 *)
coxG[{18, 1, -1, 40}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 29 2017 *)
CROSSREFS
Cf. A003945 (G.f.: (1+x)/(1-2*x)).
Sequence in context: A167648 A167881 A168680 * A168776 A168824 A168872
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved