A168743 - OEIS

A168743

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

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A170737, although the two sequences are eventually different.` `First disagreement at index 18: a(18) = 14890324713954061755033, A170737(18) = 14890324713954061755186. - Klaus Brockhaus, Mar 27 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 (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).`
	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)/(136t^18 - 16t^17 - 16t^16 - 16t^15 - 16t^14 - 16t^13 - 16t^12 - 16t^11 - 16t^10 - 16t^9 - 16t^8 - 16t^7 - 16t^6 - 16t^5 - 16t^4 - 16t^3 - 16t^2 - 16*t + 1).`
	MATHEMATICA	`With[{num=Total[2t^Range[17]]+t^18+1, den=Total[-16 t^Range[17]]+ 136t^18+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Jan 04 2012 )` `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)/(136t^18 - 16t^17 - 16t^16 - 16t^15 - 16t^14 - 16t^13 - 16t^12 - 16t^11 - 16t^10 - 16t^9 - 16t^8 - 16t^7 - 16t^6 - 16t^5 - 16t^4 - 16t^3 - 16t^2 - 16t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 10 2016 *)`
	CROSSREFS	`Cf. A170737 (G.f.: (1+x)/(1-17x)).` `Sequence in context: A167674 A167927 A168695 A168791 A168839 A168887` `Adjacent sequences: A168740 A168741 A168742 * A168744 A168745 A168746`
	KEYWORD	`nonn,easy`
	AUTHOR	`John Cannon and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`