A170478 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540946432, 2899474071552, 104381066575872, 3757718396731392, 135277862282330112, 4870003042163884032, 175320109517899825152, 6311523942644393705472

Offset

0,2

Comments

The initial terms coincide with those of A170756, 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 (35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).

Formula

G.f. (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)/(630*t^45 - 35*t^44 - 35*t^43 -

35*t^42 - 35*t^41 - 35*t^40 - 35*t^39 - 35*t^38 - 35*t^37 - 35*t^36 -

35*t^35 - 35*t^34 - 35*t^33 - 35*t^32 - 35*t^31 - 35*t^30 - 35*t^29 -

35*t^28 - 35*t^27 - 35*t^26 - 35*t^25 - 35*t^24 - 35*t^23 - 35*t^22 -

35*t^21 - 35*t^20 - 35*t^19 - 35*t^18 - 35*t^17 - 35*t^16 - 35*t^15 -

35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 -

35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1)

Mathematica

With[{num=Total[2t^Range[44]]+t^45+1, den=Total[-35 t^Range[44]]+630t^45+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Oct 14 2013 *)

Crossrefs

Sequence in context: A170334 A170382 A170430 * A170526 A170574 A170622

Adjacent sequences: A170475 A170476 A170477 * A170479 A170480 A170481

Keyword

nonn

Author

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

Status

approved