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A164350 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
1, 49, 2352, 112896, 5419008, 260112384, 12485393256, 599298819840, 28766340643992, 1380784220911872, 66277636363782144, 3181326245942132736, 152703645428292064680, 7329774290465429385408, 351829132817899422588504, 16887796785286144959221568 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170768, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..590

Index entries for linear recurrences with constant coefficients, signature (47, 47, 47, 47, 47, -1128).

FORMULA

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1128*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

a(n) = -1128*a(n-6) + 47*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

MAPLE

seq(coeff(series((1+t)*(1-t^6)/(1-48*t+1175*t^6-1128*t^7), t, n+1), t, n), n = 0..20); # G. C. Greubel, Aug 24 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^6)/(1-48*t+1175*t^6-1128*t^7), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2017 *)

coxG[{6, 1128, -47}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 24 2019 *)

PROG

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^6)/(1-48*t+1175*t^6-1128*t^7)) \\ G. C. Greubel, Sep 15 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^6)/(1-48*t+1175*t^6-1128*t^7) )); // G. C. Greubel, Aug 24 2019

(Sage)

def A164350_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^6)/(1-48*t+1175*t^6-1128*t^7)).list()

A164350_list(20) # G. C. Greubel, Aug 24 2019

(GAP) a:=[49, 2352, 112896, 5419008, 260112384, 12485393256];; for n in [7..20] do a[n]:=47*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -1128*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 24 2019

CROSSREFS

Sequence in context: A162914 A163287 A163835 * A164694 A165181 A165709

Adjacent sequences:  A164347 A164348 A164349 * A164351 A164352 A164353

KEYWORD

nonn

AUTHOR

John Cannon and N. J. A. Sloane, Dec 03 2009

STATUS

approved

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Last modified July 29 06:36 EDT 2021. Contains 346340 sequences. (Running on oeis4.)