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A170630
Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
0
1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501434880, 632170063134720, 27815482777927680, 1223881242228817920, 53850774658067988480, 2369434084954991493120, 104255099738019625697280
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170764, 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 (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
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)/(946*t^48 - 43*t^47 - 43*t^46 - 43*t^45 - 43*t^44 - 43*t^43 - 43*t^42
- 43*t^41 - 43*t^40 - 43*t^39 - 43*t^38 - 43*t^37 - 43*t^36 - 43*t^35 -
43*t^34 - 43*t^33 - 43*t^32 - 43*t^31 - 43*t^30 - 43*t^29 - 43*t^28 -
43*t^27 - 43*t^26 - 43*t^25 - 43*t^24 - 43*t^23 - 43*t^22 - 43*t^21 -
43*t^20 - 43*t^19 - 43*t^18 - 43*t^17 - 43*t^16 - 43*t^15 - 43*t^14 -
43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 -
43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1)
MATHEMATICA
coxG[{48, 946, -43}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 22 2020 *)
CROSSREFS
Sequence in context: A170486 A170534 A170582 * A170678 A170726 A170764
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved