A170390 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501434880, 632170063134720, 27815482777927680, 1223881242228817920, 53850774658067988480, 2369434084954991493120, 104255099738019625697280

Offset

0,2

Comments

The initial terms coincide with those of A170764, although the two sequences are eventually different.

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

Links

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).

Formula

G.f. (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)/(946*t^43 - 43*t^42 - 43*t^41 - 43*t^40 - 43*t^39 -

43*t^38 - 43*t^37 - 43*t^36 - 43*t^35 - 43*t^34 - 43*t^33 - 43*t^32 -

43*t^31 - 43*t^30 - 43*t^29 - 43*t^28 - 43*t^27 - 43*t^26 - 43*t^25 -

43*t^24 - 43*t^23 - 43*t^22 - 43*t^21 - 43*t^20 - 43*t^19 - 43*t^18 -

43*t^17 - 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 -

43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 -

43*t^2 - 43*t + 1)

Mathematica

With[{num=Total[2t^Range[42]]+t^43+1, den=Total[-43 t^Range[42]]+946t^43+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Mar 19 2013 *)

Crossrefs

Sequence in context: A170246 A170294 A170342 * A170438 A170486 A170534

Adjacent sequences: A170387 A170388 A170389 * A170391 A170392 A170393

Keyword

nonn

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Status

approved