A170592 - OEIS

A170592

Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

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

(list; graph; refs; listen; history; text; internal format)

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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).

FORMULA

G.f. (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)/(15*t^48 - 5*t^47 - 5*t^46 - 5*t^45 - 5*t^44 - 5*t^43 - 5*t^42 -

5*t^41 - 5*t^40 - 5*t^39 - 5*t^38 - 5*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[{48, 15, -5}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 14 2018 *)

CROSSREFS

Sequence in context: A170448 A170496 A170544 * A170640 A170688 A003949

Adjacent sequences: A170589 A170590 A170591 * A170593 A170594 A170595

KEYWORD

nonn

AUTHOR

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

STATUS

approved