A168697 - OEIS

A168697

Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964380, 44266298381323220, 841059669245141180, 15980133715657682420
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	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A170739, although the two sequences are eventually different.` `First disagreement at index 17: a(17) = 5768828271352423353430, A170739(17) = 5768828271352423353620. - Klaus Brockhaus, Mar 30 2011` `Computed with MAGMA using commands similar to those used to compute A154638.`
	LINKS	`G. C. Greubel, Table of n, a(n) for n = 0..500` `Index entries for linear recurrences with constant coefficients, signature (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).`
	FORMULA	`G.f.: (t^17 + 2t^16 + 2t^15 + 2t^14 + 2t^13 + 2t^12 + 2t^11 + 2t^10 + 2t^9 + 2t^8 + 2t^7 + 2t^6 + 2t^5 + 2t^4 + 2t^3 + 2t^2 + 2t + 1)/ (171t^17 - 18t^16 - 18t^15 - 18t^14 - 18t^13 - 18t^12 - 18t^11 - 18t^10 - 18t^9 - 18t^8 - 18t^7 - 18t^6 - 18t^5 - 18t^4 - 18t^3 - 18t^2 - 18*t + 1).`
	MATHEMATICA	`coxG[{17, 171, -18}] (* The coxG program is at A169452 ) ( Harvey P. Dale, Jun 24 2015 )` `CoefficientList[Series[(t^17 + 2t^16 + 2t^15 + 2t^14 + 2t^13 + 2t^12 + 2t^11 + 2t^10 + 2t^9 + 2t^8 + 2t^7 + 2t^6 + 2t^5 + 2t^4 + 2t^3 + 2t^2 + 2t + 1)/(171t^17 - 18t^16 - 18t^15 - 18t^14 - 18t^13 - 18t^12 - 18t^11 - 18t^10 - 18t^9 - 18t^8 - 18t^7 - 18t^6 - 18t^5 - 18t^4 - 18t^3 - 18t^2 - 18t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 03 2016 *)`
	CROSSREFS	`Cf. A170739 (G.f.: (1+x)/(1-19x)).` `Sequence in context: A167148 A167680 A167931 A168745 A168793 A168841` `Adjacent sequences: A168694 A168695 A168696 * A168698 A168699 A168700`
	KEYWORD	`nonn`
	AUTHOR	`John Cannon and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`