A168723 - OEIS

A168723

Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558593750, 1566328930136718750, 70484801856152343750, 3171816083526855468750, 142731723758708496093750 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A170765, although the two sequences are eventually different.` `First disagreement at index 17: a(17) = 13006428327512311706542967715, A170765(17) = 13006428327512311706542968750. - Klaus Brockhaus, Mar 28 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 (44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, -990).`
	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)/(990t^17 - 44t^16 - 44t^15 - 44t^14 - 44t^13 - 44t^12 - 44t^11 - 44t^10 - 44t^9 - 44t^8 - 44t^7 - 44t^6 - 44t^5 - 44t^4 - 44t^3 - 44t^2 - 44*t + 1).`
	MATHEMATICA	`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)/(990t^17 - 44t^16 - 44t^15 - 44t^14 - 44t^13 - 44t^12 - 44t^11 - 44t^10 - 44t^9 - 44t^8 - 44t^7 - 44t^6 - 44t^5 - 44t^4 - 44t^3 - 44t^2 - 44t + 1), {t, 0, 50}], t] ( G. C. Greubel, Aug 06 2016 *)`
	CROSSREFS	`Cf. A170765 (G.f.: (1+x)/(1-45x)).` `Sequence in context: A167643 A167861 A167962 A168771 A168819 A168867` `Adjacent sequences: A168720 A168721 A168722 * A168724 A168725 A168726`
	KEYWORD	`nonn`
	AUTHOR	`John Cannon and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`