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<a href="/index/Rec#order_48">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).

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_John Cannon (john(AT)maths.usyd.edu.au) _ and N. J. A. Sloane, Dec 03 2009

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With[{num=Total[2t^Range[47]]+t^48+1, den=Total[-40 t^Range[47]]+820t^48+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jan 14 2014 *)

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John Cannon (john(AT)maths.usyd.edu.au) and _N. J. A. Sloane (njas(AT)research.att.com), _, Dec 03 2009

The g.f. agrees with (1+t)/(1-41*t) for 48 terms, but after that it is different. That is, a(n) = 42*41^(n-1) for 1 <= n <= 47. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 14 2009]

G,.f.: (t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 +

nonn,new

nonn

Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859623082, 13750041244546362, 563751691026400842, 23113819332082434522, 947666592615379815402, 38854330297230572431482

0,2

The initial terms coincide with those of A170761, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

The g.f. agrees with (1+t)/(1-41*t) for 48 terms, but after that it is different. That is, a(n) = 42*41^(n-1) for 1 <= n <= 47. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 14 2009]

G,f.: (t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 +

2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +

2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +

2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +

2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +

2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +

1)/(820*t^48 - 40*t^47 - 40*t^46 - 40*t^45 - 40*t^44 - 40*t^43 - 40*t^42

- 40*t^41 - 40*t^40 - 40*t^39 - 40*t^38 - 40*t^37 - 40*t^36 - 40*t^35 -

40*t^34 - 40*t^33 - 40*t^32 - 40*t^31 - 40*t^30 - 40*t^29 - 40*t^28 -

40*t^27 - 40*t^26 - 40*t^25 - 40*t^24 - 40*t^23 - 40*t^22 - 40*t^21 -

40*t^20 - 40*t^19 - 40*t^18 - 40*t^17 - 40*t^16 - 40*t^15 - 40*t^14 -

40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 -

40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1)

nonn

John Cannon (john(AT)maths.usyd.edu.au) and N. J. A. Sloane (njas(AT)research.att.com), Dec 03 2009

approved