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A170622
Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
0
1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540946432, 2899474071552, 104381066575872, 3757718396731392, 135277862282330112, 4870003042163884032, 175320109517899825152, 6311523942644393705472
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170756, 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 (35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).
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)/(630*t^48 - 35*t^47 - 35*t^46 - 35*t^45 - 35*t^44 - 35*t^43 - 35*t^42
- 35*t^41 - 35*t^40 - 35*t^39 - 35*t^38 - 35*t^37 - 35*t^36 - 35*t^35 -
35*t^34 - 35*t^33 - 35*t^32 - 35*t^31 - 35*t^30 - 35*t^29 - 35*t^28 -
35*t^27 - 35*t^26 - 35*t^25 - 35*t^24 - 35*t^23 - 35*t^22 - 35*t^21 -
35*t^20 - 35*t^19 - 35*t^18 - 35*t^17 - 35*t^16 - 35*t^15 - 35*t^14 -
35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 -
35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1)
MATHEMATICA
coxG[{48, 630, -35}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 13 2024 *)
CROSSREFS
Sequence in context: A170478 A170526 A170574 * A170670 A170718 A170756
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved