A169187 - OEIS

A169187

Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A170749, although the two sequences are eventually different.` `First disagreement at index 27: a(27) = 3158415047555715036977934578782667751195, A170749(27) = 3158415047555715036977934578782667751630. - Klaus Brockhaus, May 07 2011` `Computed with MAGMA using commands similar to those used to compute A154638.`
	LINKS	`Table of n, a(n) for n=0..15.` `Index entries for linear recurrences with constant coefficients, signature (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).`
	FORMULA	G.f.: (t^27 + 2t^26 + 2t^25 + 2t^24 + 2t^23 + 2t^22 + 2t^21 + 2t^20 + 2t^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)/(406t^27 - 28t^26 - 28t^25 - 28t^24 - 28t^23 - 28t^22 - 28t^21 - 28t^20 - 28t^19 - 28t^18 - 28t^17 - 28t^16 - 28t^15 - 28t^14 - 28t^13 - 28t^12 - 28t^11 - 28t^10 - 28t^9 - 28t^8 - 28t^7 - 28t^6 - 28t^5 - 28t^4 - 28t^3 - 28t^2 - 28*t + 1).
	MATHEMATICA	`With[{num=Total[2t^Range[26]]+t^27+1, den=Total[-28 t^Range[26]]+ 406t^27+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Oct 21 2011 *)`
	CROSSREFS	`Cf. A170749 (G.f.: (1+x)/(1-29x)).` `Sequence in context: A169043 A169091 A169139 A169235 A169283 A169331` `Adjacent sequences: A169184 A169185 A169186 * A169188 A169189 A169190`
	KEYWORD	`nonn`
	AUTHOR	`John Cannon and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`