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Search: id:A053727
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| A053727 |
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Triangle T(n,k) = Sum_{d|GCD(n,k)} mu(d)*C(n/d,k/d) (n >= 1, 1<=k<=n). |
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+0
2
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| 1, 2, 0, 3, 3, 0, 4, 4, 4, 0, 5, 10, 10, 5, 0, 6, 12, 18, 12, 6, 0, 7, 21, 35, 35, 21, 7, 0, 8, 24, 56, 64, 56, 24, 8, 0, 9, 36, 81, 126, 126, 81, 36, 9, 0, 10, 40, 120, 200, 250, 200, 120, 40, 10, 0, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 0, 12, 60
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Triangle of number of primitive words over {0,1} of length n that contain k 1's, for n,k>=1. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 08 2004
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REFERENCES
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J.-P. Allouche and J. Shallit, Automatic sequences, Cambridge Univeristy Press, 2003, p 29
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LINKS
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Index entries for triangles and arrays related to Pascal's triangle
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EXAMPLE
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1; 2,0; 3,3,0; 4,4,4,0; 5,10,10,5,0; 6,12,18,12,6,0; ...
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PROGRAM
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(PARI) T(n, k)=sumdiv(gcd(k, n), d, moebius(d)*binomial(n/d, k/d)) (from Cloitre)
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CROSSREFS
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Cf. A042979, A042980. T(2n, n), T(2n+1, n) match A007727, A001700, respectively. Row sums match A027375.
Same triangle as A050186 except this one does not includes column 0.
Sequence in context: A099838 A127449 A138057 this_sequence A127952 A134409 A094067
Adjacent sequences: A053724 A053725 A053726 this_sequence A053728 A053729 A053730
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KEYWORD
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nonn,tabl
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AUTHOR
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njas, Mar 24 2000
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