login
A163552
Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 30, 870, 25230, 731670, 21217995, 615309240, 17843602560, 517453877640, 15005855150160, 435160887802830, 12619407316577880, 365955317872798920, 10612486887830912280, 307755817292235608520, 8924735934026717183820
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170749, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
FORMULA
G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(406*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
a(n) = 28*a(n-1)+28*a(n-2)+28*a(n-3)+28*a(n-4)-406*a(n-5). - Wesley Ivan Hurt, May 11 2021
MATHEMATICA
CoefficientList[Series[(x^5+2*x^4+2*x^3+2*x^2+2*x+1)/(406*x^5-28*x^4 - 28*x^3-28*x^2-28*x+1), {x, 0, 20}], x] (* Wesley Ivan Hurt, Mar 31 2017 *)
LinearRecurrence[{28, 28, 28, 28, -406}, {1, 30, 870, 25230, 731670, 21217995}, 20] (* Vincenzo Librandi, Apr 01 2017 *)
coxG[{5, 406, -28}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 16 2019 *)
PROG
(Magma) I:=[1, 30, 870, 25230, 731670, 21217995]; [n le 6 select I[n] else 28*Self(n-1)+28*Self(n-2)+28*Self(n-3)+28*Self(n-4)-406*Self(n-5): n in [1..30]]; // Vincenzo Librandi, Apr 01 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-29*x+434*x^5-406*x^6) )); // G. C. Greubel, May 16 2019
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-29*x+434*x^5-406*x^6)) \\ G. C. Greubel, Jul 28 2017
(Sage) ((1+x)*(1-x^5)/(1-29*x+434*x^5-406*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019
CROSSREFS
Sequence in context: A007850 A162833 A163208 * A164027 A164666 A164983
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved