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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 February 23 21:23 EST 2018. Contains 299588 sequences. (Running on oeis4.)