A170693 - OEIS

This site is supported by donations to The OEIS Foundation.

A170693

Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306572, 28295372292, 311249095212, 3423740047332, 37661140520652, 414272545727172, 4556998002998892, 50126978032987812, 551396758362865932 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A003954, 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 66. - Vincenzo Librandi, Dec 08 2012`
	LINKS	`Vincenzo Librandi, Table of n, a(n) for n = 0..20`
	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)/(55t^50 - 10t^49 - 10t^48 - 10t^47 - 10t^46 - 10t^45 -` `10t^44 - 10t^43 - 10t^42 - 10t^41 - 10t^40 - 10t^39 - 10t^38 -` `10t^37 - 10t^36 - 10t^35 - 10t^34 - 10t^33 - 10t^32 - 10t^31 -` `10t^30 - 10t^29 - 10t^28 - 10t^27 - 10t^26 - 10t^25 - 10t^24 -` `10t^23 - 10t^22 - 10t^21 - 10t^20 - 10t^19 - 10t^18 - 10t^17 -` `10t^16 - 10t^15 - 10t^14 - 10t^13 - 10t^12 - 10t^11 - 10t^10 -` `10t^9 - 10t^8 - 10t^7 - 10t^6 - 10t^5 - 10t^4 - 10t^3 - 10t^2 -` `10*t + 1)`
	MATHEMATICA	`With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-10 t^Range[49]] + 55 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Vincenzo Librandi, Dec 08 2012 *)`
	CROSSREFS	`Sequence in context: A170549 A170597 A170645 * A120673 A120674 A016123` `Adjacent sequences: A170690 A170691 A170692 * A170694 A170695 A170696`
	KEYWORD	`nonn`
	AUTHOR	`John Cannon (john(AT)maths.usyd.edu.au) and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`

Content is available under The OEIS End-User License Agreement .

Last modified June 19 19:50 EDT 2013. Contains 226416 sequences.