A169579 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248998, 4938546112212926, 182726206151878262, 6760869627619495694, 250152176221921340678, 9255630520211089605086

Offset

0,2

Comments

The initial terms coincide with those of A170757, 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 (36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, -666).

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)/(666*t^35 - 36*t^34 - 36*t^33 - 36*t^32 - 36*t^31 -

36*t^30 - 36*t^29 - 36*t^28 - 36*t^27 - 36*t^26 - 36*t^25 - 36*t^24 -

36*t^23 - 36*t^22 - 36*t^21 - 36*t^20 - 36*t^19 - 36*t^18 - 36*t^17 -

36*t^16 - 36*t^15 - 36*t^14 - 36*t^13 - 36*t^12 - 36*t^11 - 36*t^10 -

36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 -

36*t + 1)

Mathematica

coxG[{35, 666, -36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 08 2021 *)

Crossrefs

Sequence in context: A169435 A169483 A169531 * A170047 A170095 A170143

Adjacent sequences: A169576 A169577 A169578 * A169580 A169581 A169582

Keyword

nonn

Author

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

Status

approved