A169424 - OEIS

A169424

Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A170746, although the two sequences are eventually different.` `First disagreement is at index 32, the difference is 351. - Klaus Brockhaus, Jun 27 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 (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).`
	FORMULA	`G.f.: (t^32 + 2t^31 + 2t^30 + 2t^29 + 2t^28 + 2t^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)/(325t^32 - 25t^31 - 25t^30 - 25t^29 - 25t^28 - 25t^27 - 25t^26 - 25t^25 - 25t^24 - 25t^23 - 25t^22 - 25t^21 - 25t^20 - 25t^19 - 25t^18 - 25t^17 - 25t^16 - 25t^15 - 25t^14 - 25t^13 - 25t^12 -` `25t^11 - 25t^10 - 25t^9 - 25t^8 - 25t^7 - 25t^6 - 25t^5 - 25t^4 - 25t^3 - 25t^2 - 25t + 1).` `G.f.: (1+2sum(k=1..31, x^k)+x^32)/(1-25sum(k=1..31, x^k)+325x^32).`
	MATHEMATICA	`With[{num=Total[2t^Range[31]]+t^32+1, den=Total[-25 t^Range[31]]+ 325t^32+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jun 18 2012 *)`
	CROSSREFS	`Cf. A170746 (G.f.: (1+x)/(1-26x) ).` `Sequence in context: A169280 A169328 A169376 A169472 A169520 A169568` `Adjacent sequences: A169421 A169422 A169423 * A169425 A169426 A169427`
	KEYWORD	`nonn`
	AUTHOR	`John Cannon and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`