A170544 - OEIS

A170544

Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = 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, -15).

FORMULA

G.f. (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^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)

CROSSREFS

Sequence in context: A170400 A170448 A170496 * A170592 A170640 A170688

Adjacent sequences: A170541 A170542 A170543 * A170545 A170546 A170547

KEYWORD

nonn

AUTHOR

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

STATUS

approved