A168767 - OEIS

A168767

Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859623082, 13750041244546362, 563751691026400842, 23113819332082434522, 947666592615379815402, 38854330297230572431482 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A170761, although the two sequences are eventually different.` `First disagreement at index 18: a(18) = 109793051235032559584557006941, A170761(18) = 109793051235032559584557007802. - Klaus Brockhaus, Mar 26 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 (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).`
	FORMULA	`G.f.: (t^18 + 2t^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)/(820t^18 - 40t^17 - 40t^16 - 40t^15 - 40t^14 - 40t^13 - 40t^12 - 40t^11 - 40t^10 - 40t^9 - 40t^8 - 40t^7 - 40t^6 - 40t^5 - 40t^4 - 40t^3 - 40t^2 - 40*t + 1).`
	MATHEMATICA	`With[{num=Total[2t^Range[17]]+t^18+1, den=Total[-40 t^Range[17]]+ 820t^18+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Oct 25 2011 )` `CoefficientList[Series[(t^18 + 2t^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)/(820t^18 - 40t^17 - 40t^16 - 40t^15 - 40t^14 - 40t^13 - 40t^12 - 40t^11 - 40t^10 - 40t^9 - 40t^8 - 40t^7 - 40t^6 - 40t^5 - 40t^4 - 40t^3 - 40t^2 - 40t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 11 2016 *)`
	CROSSREFS	`Cf. A170761 (G.f.: (1+x)/(1-41x)).` `Sequence in context: A167848 A167958 A168719 A168815 A168863 A168911` `Adjacent sequences: A168764 A168765 A168766 * A168768 A168769 A168770`
	KEYWORD	`nonn,easy`
	AUTHOR	`John Cannon and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`