A170095 - OEIS

A170095

Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248998, 4938546112212926, 182726206151878262, 6760869627619495694, 250152176221921340678, 9255630520211089605086, 342458329247810315388182, 12670958182168981669362734, 468825452740252321766421158

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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..17.

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, 36, 36, -666).

FORMULA

G.f.: (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)/(666*t^37 - 36*t^36 - 36*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[{37, 666, -36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 04 2023 *)

CROSSREFS

Sequence in context: A170671 A170719 A170757 * A218740 A158702 A239364

Adjacent sequences: A170092 A170093 A170094 * A170096 A170097 A170098

KEYWORD

nonn,easy

AUTHOR

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

EXTENSIONS

a(15)-a(17) from Stefano Spezia, Feb 02 2026

STATUS

approved