A168833 - OEIS

A168833

Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = 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.` `First disagreement at index 20: a(20) = 733909085380974555426, A003954(20) = 733909085380974555492. - Klaus Brockhaus, Apr 02 2011` `Computed with MAGMA using commands similar to those used to compute A154638.`
	LINKS	`G. C. Greubel, Table of n, a(n) for n = 0..955` `Index entries for linear recurrences with constant coefficients, signature (10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, -55).`
	FORMULA	`G.f.: (t^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^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	`CoefficientList[Series[(t^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^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 - 10t + 1), {t, 0, 100}], t] ( G. C. Greubel, Nov 22 2016 )` `coxG[{20, 55, -10}] ( The coxG program is at A169452 ) ( Harvey P. Dale, Apr 20 2022 *)`
	CROSSREFS	`Cf. A003954 (G.f.: (1+x)/(1-11x)).` `Sequence in context: A168689 A168737 A168785 A168881 A168929 A168977` `Adjacent sequences: A168830 A168831 A168832 * A168834 A168835 A168836`
	KEYWORD	`nonn`
	AUTHOR	`John Cannon and N. J. A. Sloane, Dec 03 2009`
	STATUS	`approved`