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A170648
Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
0
1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701760, 4338819824640, 60743477544960, 850408685629440, 11905721598812160, 166680102383370240, 2333521433367183360
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170734, 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 (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, -91).
FORMULA
G.f.: (t^49 + 2*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)/(91*t^49 - 13*t^48 - 13*t^47 - 13*t^46 - 13*t^45 - 13*t^44 - 13*t^43
- 13*t^42 - 13*t^41 - 13*t^40 - 13*t^39 - 13*t^38 - 13*t^37 - 13*t^36 -
13*t^35 - 13*t^34 - 13*t^33 - 13*t^32 - 13*t^31 - 13*t^30 - 13*t^29 -
13*t^28 - 13*t^27 - 13*t^26 - 13*t^25 - 13*t^24 - 13*t^23 - 13*t^22 -
13*t^21 - 13*t^20 - 13*t^19 - 13*t^18 - 13*t^17 - 13*t^16 - 13*t^15 -
13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 -
13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).
a(n) = -91*a(n-49) + 13*Sum_{k=1..48} a(n-k). - Wesley Ivan Hurt, May 04 2024
MATHEMATICA
coxG[{49, 91, -13}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 24 2024 *)
CROSSREFS
Sequence in context: A170504 A170552 A170600 * A170696 A170734 A186231
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved