A169091 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430

Offset

0,2

Comments

The initial terms coincide with those of A170749, although the two sequences are eventually different.

First disagreement at index 25: a(25) = 3755547024441991720544511984283789995, A170749(25) = 3755547024441991720544511984283790430. - Klaus Brockhaus, Apr 25 2011

Computed with MAGMA using commands similar to those used to compute A154638.

Links

Robert Israel, Table of n, a(n) for n = 0..683

Index entries for linear recurrences with constant coefficients, signature (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).

Formula

G.f.: (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)/(406*t^25 - 28*t^24 - 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

Mathematica

coxG[{25, 406, -28}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 05 2015 *)

Crossrefs

Cf. A170749 (G.f.: (1+x)/(1-29*x)).

Sequence in context: A168947 A168995 A169043 * A169139 A169187 A169235

Adjacent sequences: A169088 A169089 A169090 * A169092 A169093 A169094

Keyword

nonn

Author

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

Status

approved