A170064 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543872, 423263232, 2539579392, 15237476352, 91424858112, 548549148672, 3291294892032, 19747769352192, 118486616113152, 710919696678912, 4265518180073472

Offset

0,2

Comments

The initial terms coincide with those of A003949, 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..20.

Index entries for linear recurrences with constant coefficients, signature (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).

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)/(15*t^37 - 5*t^36 - 5*t^35 -

5*t^34 - 5*t^33 - 5*t^32 - 5*t^31 - 5*t^30 - 5*t^29 - 5*t^28 - 5*t^27 -

5*t^26 - 5*t^25 - 5*t^24 - 5*t^23 - 5*t^22 - 5*t^21 - 5*t^20 - 5*t^19 -

5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 -

5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 -

5*t + 1)

Mathematica

coxG[{37, 15, -5}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 31 2021 *)

Crossrefs

Sequence in context: A169500 A169548 A170016 * A170112 A170160 A170208

Adjacent sequences: A170061 A170062 A170063 * A170065 A170066 A170067

Keyword

nonn

Author

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

Status

approved