A168810 - OEIS

A168810

Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540946432, 2899474071552, 104381066575872, 3757718396731392, 135277862282330112, 4870003042163884032, 175320109517899825152, 6311523942644393705472 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A170756, although the two sequences are eventually different.` `First disagreement at index 19: a(19) = 381633717544149815208362114406, A170756(19) = 381633717544149815208362115072. - Klaus Brockhaus, Apr 01 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 (35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).`
	FORMULA	`G.f.: (t^19 + 2t^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)/(630t^19 - 35t^18 - 35t^17 - 35t^16 - 35t^15 - 35t^14 - 35t^13 - 35t^12 - 35t^11 - 35t^10 - 35t^9 - 35t^8 - 35t^7 - 35t^6 - 35t^5 - 35t^4 - 35t^3 - 35t^2 - 35*t + 1).`
	MATHEMATICA	`CoefficientList[Series[(t^19 + 2t^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)/(630t^19 - 35t^18 - 35t^17 - 35t^16 - 35t^15 - 35t^14 - 35t^13 - 35t^12 - 35t^11 - 35t^10 - 35t^9 - 35t^8 - 35t^7 - 35t^6 - 35t^5 - 35t^4 - 35t^3 - 35t^2 - 35t + 1), {t, 0, 50}], t] ( G. C. Greubel, Aug 17 2016 *)`
	CROSSREFS	`Cf. A170756 (G.f.: (1+x)/(1-36x)).` `Sequence in context: A167953 A168714 A168762 A168858 A168906 A168954` `Adjacent sequences: A168807 A168808 A168809 * A168811 A168812 A168813`
	KEYWORD	`nonn`
	AUTHOR	`John Cannon and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`