A169285 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272

Offset

0,2

Comments

The initial terms coincide with those of A170751, although the two sequences are eventually different.

First disagreement at index 29: a(29) = 18334851874161443075947117482793396401376816, A170751(29) = 18334851874161443075947117482793396401377312. - Klaus Brockhaus, Jun 03 2011

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

Links

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).

Formula

G.f.: (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)/(465*t^29 - 30*t^28 - 30*t^27 - 30*t^26 - 30*t^25 - 30*t^24 - 30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 - 30*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

Crossrefs

Cf. A170751 (G.f.: (1+x)/(1-31*x)).

Sequence in context: A169141 A169189 A169237 * A169333 A169381 A169429

Adjacent sequences: A169282 A169283 A169284 * A169286 A169287 A169288

Keyword

nonn

Author

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

Status

approved