A170724 - OEIS

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A170724

Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505527296, 734448519232146432, 30846837807750150144, 1295567187925506306048, 54413821892871264854016 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A170762, although the two sequences are eventually different.` `Computed with MAGMA using commands similar to those used to compute A154638.` `About the initial comment, first disagreement is at index 50 and the difference is 903. - Vincenzo Librandi, Dec 07 2012`
	LINKS	`Vincenzo Librandi, Table of n, a(n) for n = 0..200`
	FORMULA	`G.f. (t^50 + 2t^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)/(861t^50 - 41t^49 - 41t^48 - 41t^47 - 41t^46 - 41t^45 -` `41t^44 - 41t^43 - 41t^42 - 41t^41 - 41t^40 - 41t^39 - 41t^38 -` `41t^37 - 41t^36 - 41t^35 - 41t^34 - 41t^33 - 41t^32 - 41t^31 -` `41t^30 - 41t^29 - 41t^28 - 41t^27 - 41t^26 - 41t^25 - 41t^24 -` `41t^23 - 41t^22 - 41t^21 - 41t^20 - 41t^19 - 41t^18 - 41t^17 -` `41t^16 - 41t^15 - 41t^14 - 41t^13 - 41t^12 - 41t^11 - 41t^10 -` `41t^9 - 41t^8 - 41t^7 - 41t^6 - 41t^5 - 41t^4 - 41t^3 - 41t^2 -` `41*t + 1)`
	MATHEMATICA	`With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-41 t^Range[49]] + 861 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Vincenzo Librandi, Dec 07 2012 *)`
	CROSSREFS	`Sequence in context: A170580 A170628 A170676 * A170762 A218745 A009987` `Adjacent sequences: A170721 A170722 A170723 * A170725 A170726 A170727`
	KEYWORD	`nonn`
	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 May 21 11:29 EDT 2013. Contains 225478 sequences.