A168749 - OEIS

A168749

Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127576, 22867434189934248, 525950986368487704, 12096872686475217192, 278228071788929995416 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A170743, although the two sequences are eventually different.` `First disagreement at index 18: a(18) = 3385200949455911254226196, A170743(18) = 3385200949455911254226472. - 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 (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).`
	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)/(253t^18 - 22t^17 - 22t^16 - 22t^15 - 22t^14 - 22t^13 - 22t^12 - 22t^11 - 22t^10 - 22t^9 - 22t^8 - 22t^7 - 22t^6 - 22t^5 - 22t^4 - 22t^3 - 22t^2 - 22*t + 1).`
	MATHEMATICA	`coxG[{18, 253, -22}] (* The coxG program is at A169452 ) ( Harvey P. Dale, Dec 19 2014 )` `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)/(253t^18 - 22t^17 - 22t^16 - 22t^15 - 22t^14 - 22t^13 - 22t^12 - 22t^11 - 22t^10 - 22t^9 - 22t^8 - 22t^7 - 22t^6 - 22t^5 - 22t^4 - 22t^3 - 22t^2 - 22t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 10 2016 *)`
	CROSSREFS	`Cf. A170743 (G.f.: (1+x)/(1-23x)).` `Sequence in context: A167695 A167938 A168701 A168797 A168845 A168893` `Adjacent sequences: A168746 A168747 A168748 * A168750 A168751 A168752`
	KEYWORD	`nonn,easy`
	AUTHOR	`John Cannon and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`