A170679 - OEIS

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A170679

Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558593750, 1566328930136718750, 70484801856152343750, 3171816083526855468750, 142731723758708496093750 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A170765, although the two sequences are eventually different.` `First disagreement is at index 49, the difference is 1035. - Klaus Brockhaus, Jun 14 2011` `Computed with MAGMA using commands similar to those used to compute A154638.`
	LINKS	`Table of n, a(n) for n=0..14.` `Index to sequences with linear recurrences with constant coefficients, order 49.`
	FORMULA	G.f.: (t^49 + 2t^48 + 2t^47 + 2t^46 + 2t^45 + 2t^44 + 2t^43 + 2t^42 + 2t^41 + 2t^40 + 2t^39 + 2t^38 + 2t^37 + 2t^36 + 2t^35 + 2t^34 + 2t^33 + 2t^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)/(990t^49 - 44t^48 - 44t^47 - 44t^46 - 44t^45 - 44t^44 - 44t^43 - 44t^42 - 44t^41 - 44t^40 - 44t^39 - 44t^38 - 44t^37 - 44t^36 - 44t^35 - 44t^34 - 44t^33 - 44t^32 - 44t^31 - 44t^30 - 44t^29 - 44t^28 - 44t^27 - 44t^26 - 44t^25 - 44t^24 - 44t^23 - 44t^22 - 44t^21 - 44t^20 - 44t^19 - 44t^18 - 44t^17 - 44t^16 - 44t^15 - 44t^14 - 44t^13 - 44t^12 - 44t^11 - 44t^10 - 44t^9 - 44t^8 - 44t^7 - 44t^6 - 44t^5 - 44t^4 - 44t^3 - 44t^2 - 44*t + 1).
	MATHEMATICA	`With[{num=Total[2t^Range[48]]+t^49+1, den=Total[-44 t^Range[48]]+1+ 990t^49}, CoefficientList[Series[num/den, {t, 0, 21}], t]] (* From Harvey P. Dale, June 14 2011 *)`
	CROSSREFS	`Cf. A170765 (G.f.: (1+x)/(1-45x).` `Sequence in context: A170583 A170631 A170727 A170765 A218748 A158752` `Adjacent sequences: A170676 A170677 A170678 * A170680 A170681 A170682`
	KEYWORD	`nonn,easy`
	AUTHOR	`John Cannon (john(AT)maths.usyd.edu.au) and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`

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Last modified June 20 05:50 EDT 2013. Contains 226419 sequences.