A169569 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852

Offset

0,2

Comments

The initial terms coincide with those of A170747, 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 (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).

Formula

G.f. (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)/(351*t^35 - 26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 -

26*t^30 - 26*t^29 - 26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 -

26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 -

26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 -

26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 -

26*t + 1)

Mathematica

coxG[{35, 351, -26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 01 2021 *)

Crossrefs

Sequence in context: A169425 A169473 A169521 * A170037 A170085 A170133

Adjacent sequences: A169566 A169567 A169568 * A169570 A169571 A169572

Keyword

nonn

Author

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

Status

approved