A168812 - OEIS

A168812

Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518976, 4462207721088, 169563893401344, 6443427949251072, 244850262071540736, 9304309958718547968, 353563778431304822784, 13435423580389583265792 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A170758, although the two sequences are eventually different.` `First disagreement at index 19: a(19) = 1064558044543330135515017772315, A170758(19) = 1064558044543330135515017773056. - 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 (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).`
	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)/(703t^19 - 37t^18 - 37t^17 - 37t^16 - 37t^15 - 37t^14 - 37t^13 - 37t^12 - 37t^11 - 37t^10 - 37t^9 - 37t^8 - 37t^7 - 37t^6 - 37t^5 - 37t^4 - 37t^3 - 37t^2 - 37*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)/(703t^19 - 37t^18 - 37t^17 - 37t^16 - 37t^15 - 37t^14 - 37t^13 - 37t^12 - 37t^11 - 37t^10 - 37t^9 - 37t^8 - 37t^7 - 37t^6 - 37t^5 - 37t^4 - 37t^3 - 37t^2 - 37t + 1), {t, 0, 50}], t] ( G. C. Greubel, Aug 17 2016 )` `coxG[{19, 703, -37}] ( The coxG program is at A169452 ) ( Harvey P. Dale, Feb 13 2018 *)`
	CROSSREFS	`Cf. A170758 (G.f.: (1+x)/(1-38x)).` `Sequence in context: A167955 A168716 A168764 A168860 A168908 A168956` `Adjacent sequences: A168809 A168810 A168811 * A168813 A168814 A168815`
	KEYWORD	`nonn`
	AUTHOR	`John Cannon and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`