A170665 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272

Offset

0,2

Comments

The initial terms coincide with those of A170751, 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..15.

Index entries for linear recurrences with constant coefficients, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).

Formula

G.f. (t^49 + 2*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)/(465*t^49 - 30*t^48 - 30*t^47 - 30*t^46 - 30*t^45 - 30*t^44 - 30*t^43

- 30*t^42 - 30*t^41 - 30*t^40 - 30*t^39 - 30*t^38 - 30*t^37 - 30*t^36 -

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

30*t^28 - 30*t^27 - 30*t^26 - 30*t^25 - 30*t^24 - 30*t^23 - 30*t^22 -

30*t^21 - 30*t^20 - 30*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 -

30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 -

30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1)

Mathematica

With[{num=Total[2t^Range[48]]+t^49+1, den=Total[-30 t^Range[48]]+465t^49+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Aug 13 2014 *)
coxG[{49, 465, -30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 08 2025 *)

Crossrefs

Sequence in context: A170521 A170569 A170617 * A170713 A170751 A218734

Adjacent sequences: A170662 A170663 A170664 * A170666 A170667 A170668

Keyword

nonn

Author

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

Status

approved