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A170590
Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
0
1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520, 83886080, 335544320, 1342177280, 5368709120, 21474836480, 85899345920, 343597383680, 1374389534720, 5497558138880, 21990232555520, 87960930222080
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003947, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).
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)/(6*t^48
- 3*t^47 - 3*t^46 - 3*t^45 - 3*t^44 - 3*t^43 - 3*t^42 - 3*t^41 - 3*t^40
- 3*t^39 - 3*t^38 - 3*t^37 - 3*t^36 - 3*t^35 - 3*t^34 - 3*t^33 - 3*t^32
- 3*t^31 - 3*t^30 - 3*t^29 - 3*t^28 - 3*t^27 - 3*t^26 - 3*t^25 - 3*t^24
- 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 - 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16
- 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 -
3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1)
MATHEMATICA
coxG[{48, 6, -3, 30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 26 2019 *)
CROSSREFS
Sequence in context: A170446 A170494 A170542 * A170638 A170686 A003947
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved