Search: id:A074650
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%I A074650
%S A074650 1,2,0,3,1,0,4,3,2,0,5,6,8,3,0,6,10,20,18,6,0,7,15,40,60,48,9,0,8,21,
%T A074650 70,150,204,116,18,0,9,28,112,315,624,670,312,30,0,10,36,168,588,1554,
%U A074650 2580,2340,810,56,0,11,45,240,1008,3360,7735,11160,8160,2184,99,0,12
%N A074650 Table T(n,k) by antidiagonals. Number of Lyndon words (aperiodic necklaces) 
               with n beads of k colors.
%D A074650 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like 
               Structures, Cambridge, 1998, pg 97 (2.3.74)
%H A074650 <a href="Sindx_Lu.html#Lyndon">Index entries for sequences related to 
               Lyndon words</a>
%F A074650 T(n, k) = (1/n) * Sum ( mu(n/d)*k^d ), d|n
%F A074650 T(n, k) = ( k^n - Sum_{d<n,d|n} d*T(d,k) ) / n - Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Mar 28 2008
%e A074650 1 2 3 4 5 ...
%e A074650 0 1 3 6 10 ...
%e A074650 0 2 8 20 40 ...
%e A074650 0 3 18 60 150 ...
%e A074650 0 6 48 204 624 ...
%p A074650 with (numtheory): T := proc (n,k) add(mobius(n/d)*k^d, d=divisors(n))/
               n end; seq (seq(T(i,d-i), i=1..d-1), d=2..12); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Mar 28 2008
%Y A074650 Columns 2-12: A001037, A027376, A027377, A001692, A032164, A001693, A027380, 
               A027381, A032165, A032166, A032167.
%Y A074650 Rows 1-4: A000027, A000217(n-1), A007290(n+1), A006011.
%Y A074650 Diagonal: A075147.
%Y A074650 See also A102659.
%Y A074650 Sequence in context: A098862 A003988 A144257 this_sequence A144955 A002187 
               A124756
%Y A074650 Adjacent sequences: A074647 A074648 A074649 this_sequence A074651 A074652 
               A074653
%K A074650 nonn,tabl
%O A074650 1,2
%A A074650 Christian G. Bower (bowerc(AT)usa.net), Aug 28 2002

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