The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A166421 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A166421

Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
(history; published version)

#16 by Michael De Vlieger at Thu Jul 25 14:48:42 EDT 2024

STATUS

reviewed

approved

#15 by Stefano Spezia at Thu Jul 25 14:15:54 EDT 2024

STATUS

proposed

reviewed

#14 by G. C. Greubel at Thu Jul 25 14:02:25 EDT 2024

STATUS

editing

proposed

#13 by G. C. Greubel at Thu Jul 25 14:02:17 EDT 2024

LINKS

<a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).

FORMULA

From G. C. Greubel, Jan 17 2023: (Start)

a(n) = 25*Sum_{j=1..10} a(n-j) - 325*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 26*x + 350*x^11 - 325*x^12). (End)

MATHEMATICA

CoefficientList[Series[(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)/(325*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1 ), {t, 0, 50}], t] (* G. C. Greubel, May 13 2016 *)

With[{p=325, q=25}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(q+1)*t + (p+q)*t^11-p*t^12), {t, 0, 40}], t]] (* G. C. Greubel, May 13 2016; Jul 25 2024 *)

PROG

(Magma)

R<x>:=PowerSeriesRing(Integers(), 30);

Coefficients(R!( (1+x)*(1-x^11)/(1-26*x+350*x^11-325*x^12) )); // G. C. Greubel, Jul 25 2024

(SageMath)

def A166421_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( (1+x)*(1-x^11)/(1-26*x+350*x^11-325*x^12) ).list()

A166421_list(30) # G. C. Greubel, Jul 25 2024

CROSSREFS

Cf. A154638, A169452, A170746.

STATUS

approved

editing

#12 by Harvey P. Dale at Sat May 22 18:13:50 EDT 2021

STATUS

editing

approved

#11 by Harvey P. Dale at Sat May 22 18:13:47 EDT 2021

MATHEMATICA

coxG[{11, 325, -25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 22 2021 *)

STATUS

approved

editing

#10 by Ray Chandler at Thu Nov 24 09:25:49 EST 2016

STATUS

editing

approved

#9 by Ray Chandler at Thu Nov 24 09:25:45 EST 2016

LINKS

<a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).

STATUS

approved

editing

#8 by Joerg Arndt at Sat May 14 01:57:55 EDT 2016

STATUS

reviewed

approved

#7 by Michel Marcus at Fri May 13 14:24:16 EDT 2016

STATUS

proposed

reviewed