A167818 - OEIS

A167818

Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540946432, 2899474071552, 104381066575872, 3757718396731392, 135277862282330112, 4870003042163884032, 175320109517899825152, 6311523942644393705472 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The initial terms coincide with those of A170756, although the two sequences start to be different at a(15).` `Computed with MAGMA using commands similar to those used to compute A154638.`
	LINKS	`G. C. Greubel, Table of n, a(n) for n = 0..500` `Index entries for linear recurrences with constant coefficients, signature (35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).`
	FORMULA	`G.f.: (t^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)/(630t^15 - 35t^14 - 35t^13 - 35t^12 - 35t^11 - 35t^10 - 35t^9 - 35t^8 - 35t^7 - 35t^6 - 35t^5 - 35t^4 - 35t^3 - 35t^2 - 35*t + 1).`
	MAPLE	`(t^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)/(630t^15 - 35t^14 - 35t^13 - 35t^12 - 35t^11 - 35t^10 - 35t^9 - 35t^8 - 35t^7 - 35t^6 - 35t^5 - 35t^4 - 35t^3 - 35t^2 - 35*t + 1);` `taylor(%, t=0, 64) ;` `gfun[seriestolist](%) ; # R. J. Mathar, Apr 12 2019`
	MATHEMATICA	`coxG[{15, 630, -35}] (* The coxG program is at A169452 ) ( Harvey P. Dale, Oct 19 2014 )` `CoefficientList[Series[(t^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)/(630t^15 - 35t^14 - 35t^13 - 35t^12 - 35t^11 - 35t^10 - 35t^9 - 35t^8 - 35t^7 - 35t^6 - 35t^5 - 35t^4 - 35t^3 - 35t^2 - 35t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 27 2016 *)`
	CROSSREFS	`Sequence in context: A166689 A167090 A167468 * A167953 A168714 A168762` `Adjacent sequences: A167815 A167816 A167817 * A167819 A167820 A167821`
	KEYWORD	`nonn`
	AUTHOR	`John Cannon and N. J. A. Sloane, Dec 03 2009`
	EXTENSIONS	`Programs and 500-term b-file confirmed by Robert Israel and Vaclav Kotesovec, Apr 11 2019`
	STATUS	`approved`