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 A123223 Triangle read by rows: T(n,k) = number of ternary Lyndon words of length n with exactly k 1's 3
 1, 2, 1, 1, 2, 0, 2, 4, 2, 0, 3, 8, 5, 2, 0, 6, 16, 16, 8, 2, 0, 9, 32, 38, 26, 9, 2, 0, 18, 64, 96, 80, 40, 12, 2, 0, 30, 128, 220, 224, 137, 56, 13, 2, 0, 56, 256, 512, 596, 448, 224, 74, 16, 2, 0, 99, 512, 1144, 1536, 1336, 806, 332, 96, 17, 2, 0, 186, 1024, 2560, 3840, 3840 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sum of rows equal to number of ternary Lyndon words A027376 first column (k=0) is equal to the number of binary Lyndon words A001037 third through sixth column (k=2,3,4,5) equal to A124720, A124721, A124722, A124723 T(n+1,n-1) entry equal to A042948 LINKS Alois P. Heinz, Rows n = 0..140, flattened FORMULA G.f. for columns (except for k=0) given by 1/k*sum_{d|k} mu(d) x^k/(1-2*x^d)^(k/d) T(0,0) = 1 and T(n,0) = 1/n*sum_{d|n} mu(d)*2^(n/d) T(n,n) = 0 if n>1, T(n,n-1) = 2 EXAMPLE Triangle begins: 1, 2,1, 1,2,0, 2,4,2,0, 3,8,5,2,0, 6,16,16,8,2,0, 9,32,38,26,9,2,0, 18,64,96,80,40,12,2,0, T(n,1) = 2^(n-1) because all words beginning with a 1 and consisting of the rest 2's or 3's are ternary Lyndon words with exactly one 1. CROSSREFS Cf. A027376, A001037, A124720, A124721, A124722, A124723, A051168, A042948. Sequence in context: A055138 A177717 A155997 * A088226 A244658 A117586 Adjacent sequences:  A123220 A123221 A123222 * A123224 A123225 A123226 KEYWORD nonn,tabl AUTHOR Mike Zabrocki, Nov 05 2006 STATUS approved

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Last modified October 15 21:06 EDT 2018. Contains 316237 sequences. (Running on oeis4.)