A170438 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = 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, 43, -946).

Formula

G.f. (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)/(946*t^44 - 43*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[43]]+t^44+1, den=Total[-43 t^Range[43]]+946t^44+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Sep 29 2013 *)

Crossrefs

Sequence in context: A170294 A170342 A170390 * A170486 A170534 A170582

Adjacent sequences: A170435 A170436 A170437 * A170439 A170440 A170441

Keyword

nonn

Author

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

Status

approved