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A165216
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Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.
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0
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1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994908, 1207958976, 9663669540, 77309338176, 618474560256, 4947795320832, 39582353276928, 316658751897600, 2533269420638208, 20266150608766188, 162129166819422768
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.
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FORMULA
| G.f. (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^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)
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MATHEMATICA
| With[{num=Total[2t^Range[8]]+t^9+1, den=Total[-7 t^Range[8]]+ 28t^9+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* From Harvey P. Dale, Oct 02 2011 *)
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CROSSREFS
| Sequence in context: A163953 A164375 A164777 * A165787 A166367 A166541
Adjacent sequences: A165213 A165214 A165215 * A165217 A165218 A165219
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KEYWORD
| nonn
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AUTHOR
| John Cannon (john(AT)maths.usyd.edu.au) and N. J. A. Sloane (njas(AT)research.att.com), Dec 03 2009
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