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A104000 Square array T(r,m) read by antidiagonals: number of cyclically reduced words of length m in F_r. 0

%I #4 May 20 2013 09:01:11

%S 2,4,2,6,12,2,8,30,28,2,10,56,126,84,2,12,90,344,630,244,2,14,132,730,

%T 2408,3126,732,2,16,182,1332,6570,16808,15630,2188,2,18,240,2198,

%U 14652,59050,117656,78126,6564,2,20,306,3376,28574,161052,531450

%N Square array T(r,m) read by antidiagonals: number of cyclically reduced words of length m in F_r.

%H I. Rivin, <a href="http://arXiv.org/abs/math.CO/9911076">Growth in free groups (and other stories)</a>

%F T(r, m) = (2r-1)^m + 1 + (r-1)(1+(-1)^m).

%e 2,2,2,2,2,2,2,2,2,

%e 4,12,28,84,244,732,2188,6564,19684,

%e 6,30,126,630,3126,15630,78126,390630,1953126,

%e 8,56,344,2408,16808,117656,823544,5764808,40353608,

%e 10,90,730,6570,59050,531450,4782970,43046730,387420490,

%e 12,132,1332,14652,161052,1771572,19487172,214358892,2357947692,

%e 14,182,2198,28574,371294,4826822,62748518,815730734,10604499374,

%K nonn,tabl

%O 1,1

%A _Ralf Stephan_, Feb 26 2005

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