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A169426
Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
0
1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951744, 306775222648832, 8589706234167296, 240511774556684288, 6734329687587160064, 188561231252440481792, 5279714475068333490176
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170748, although the two sequences are eventually different.
First disagreement is at index 32, the difference is 406. - Klaus Brockhaus, Jun 27 2011
Computed with Magma using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).
FORMULA
G.f.: (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)/(378*t^32 - 27*t^31 - 27*t^30 - 27*t^29 - 27*t^28 - 27*t^27 - 27*t^26 - 27*t^25 - 27*t^24 - 27*t^23 - 27*t^22 - 27*t^21 - 27*t^20 - 27*t^19 - 27*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-27*sum(k=1..31, x^k)+378*x^32).
CROSSREFS
Cf. A170748 (G.f.: (1+x)/(1-28*x) ).
Sequence in context: A169282 A169330 A169378 * A169474 A169522 A169570
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved