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 A143325 Table T(n,k) by antidiagonals. T(n,k) is the number of length n primitive (=aperiodic or period n) k-ary words (n,k >= 1) which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet. 23
 1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 8, 6, 0, 1, 4, 15, 24, 15, 0, 1, 5, 24, 60, 80, 27, 0, 1, 6, 35, 120, 255, 232, 63, 0, 1, 7, 48, 210, 624, 1005, 728, 120, 0, 1, 8, 63, 336, 1295, 3096, 4095, 2160, 252, 0, 1, 9, 80, 504, 2400, 7735, 15624, 16320, 6552, 495, 0, 1, 10, 99 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Column k is Dirichlet convolution of mu(n) with k^(n-1). The coefficients of the polynomial of row n are given by the n-th row of triangle A054525; for example row 4 has polynomial -k+k^3. LINKS Alois P. Heinz, Antidiagonals n = 1..141, flattened FORMULA T(n,k) = Sum_{d|n} k^(d-1) * mu(n/d). T(n,k) = k^(n-1) - Sum_{d f1(n)(k); seq(seq(T(n, 1+d-n), n=1..d), d=1..12); MATHEMATICA t[n_, k_] := Sum[k^(d-1)*MoebiusMu[n/d], {d, Divisors[n]}]; Table[t[n-k+1, k], {n, 1, 12}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Jan 21 2014, from first formula *) CROSSREFS Columns k=1-10 give: A063524, A000740, A034741, A295505, A295506, A320071, A320072, A320073, A320074, A320075. Rows n=1-5, 7 give: A000012, A001477, A005563, A007531, A123865, A123866. Main diagonal gives A075147. Cf. A074650, A143324, A008683, A054525. Sequence in context: A255961 A297328 A055137 * A307910 A128888 A305401 Adjacent sequences:  A143322 A143323 A143324 * A143326 A143327 A143328 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Aug 07 2008 STATUS approved

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Last modified January 26 05:10 EST 2020. Contains 331273 sequences. (Running on oeis4.)