A169358 - OEIS

A169358

Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959552, 9663676416, 77309411328, 618475290624, 4947802324992, 39582418599936, 316659348799488, 2533274790395904, 20266198323167232, 162129586585337856 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A003951, although the two sequences are eventually different.` `First disagreement at index 31: a(31) = 11141460353568422474092117980, A003951(31) = 11141460353568422474092118016. - Klaus Brockhaus, Jun 17 2011` `Computed with Magma using commands similar to those used to compute A154638.`
	LINKS	`Table of n, a(n) for n=0..19.` `Index entries for linear recurrences with constant coefficients, signature (7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,-28).`
	FORMULA	G.f.: (t^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)/(28t^31 - 7t^30 - 7t^29 - 7t^28 - 7t^27 - 7t^26 - 7t^25 - 7t^24 - 7t^23 - 7t^22 - 7t^21 - 7t^20 - 7t^19 - 7t^18 - 7t^17 - 7t^16 - 7t^15 - 7t^14 - 7t^13 - 7t^12 - 7t^11 - 7t^10 - 7t^9 - 7t^8 - 7t^7 - 7t^6 - 7t^5 - 7t^4 - 7t^3 - 7t^2 - 7t + 1). `a(n) = -28a(n-31) + 7*Sum_{k=1..30} a(n-k). - Wesley Ivan Hurt, Apr 26 2021`
	CROSSREFS	`Cf. A003951 (G.f.: (1+x)/(1-8x)).` `Sequence in context: A169214 A169262 A169310 A169406 A169454 A169502` `Adjacent sequences: A169355 A169356 A169357 * A169359 A169360 A169361`
	KEYWORD	`nonn`
	AUTHOR	`John Cannon and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`