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A170597 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I. 0
1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306572, 28295372292, 311249095212, 3423740047332, 37661140520652, 414272545727172, 4556998002998892, 50126978032987812, 551396758362865932 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003954, 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 (10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, -55).
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)/(55*t^48 - 10*t^47 - 10*t^46 - 10*t^45 - 10*t^44 - 10*t^43 - 10*t^42
- 10*t^41 - 10*t^40 - 10*t^39 - 10*t^38 - 10*t^37 - 10*t^36 - 10*t^35 -
10*t^34 - 10*t^33 - 10*t^32 - 10*t^31 - 10*t^30 - 10*t^29 - 10*t^28 -
10*t^27 - 10*t^26 - 10*t^25 - 10*t^24 - 10*t^23 - 10*t^22 - 10*t^21 -
10*t^20 - 10*t^19 - 10*t^18 - 10*t^17 - 10*t^16 - 10*t^15 - 10*t^14 -
10*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 -
10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1)
MATHEMATICA
coxG[{48, 55, -10}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 02 2021 *)
CROSSREFS
Sequence in context: A170453 A170501 A170549 * A170645 A170693 A120673
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)