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A050870
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T(h,k) = binomial(h,k) - A050186(h,k).
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4
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0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 3, 2, 3, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 4, 0, 6, 0, 4, 0, 1, 1, 0, 0, 3, 0, 0, 3, 0, 0, 1, 1, 0, 5, 0, 10, 2, 10, 0, 5, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 6, 4, 15, 0, 24, 0, 15, 4, 6, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 7, 0, 21, 0, 35, 2, 35, 0, 21, 0, 7, 0, 1, 1, 0
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OFFSET
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0,13
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COMMENTS
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T(h,k) = number of periodic binary words of k 1's and h-k 0's.
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LINKS
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EXAMPLE
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0;
0,0;
1,0,1;
1,0,0,1;
1,0,2,0,1;
1,0,0,0,0,1;
1,0,3,2,3,0,1;
1,0,0,0,0,0,0,1;
1,0,4,0,6,0,4,0,1;
1,0,0,3,0,0,3,0,0,1;
1,0,5,0,10,2,10,0,5,0,1;
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MAPLE
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if n = 0 then
1;
else
add (numtheory[mobius](d)*binomial(n/d, k/d), d =numtheory[divisors](igcd(n, k))) ;
end if;
end proc:
end proc:
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MATHEMATICA
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T[n_, k_] := Binomial[n, k] - If[n == 0, 1, Sum[MoebiusMu[d] Binomial[n/d, k/d], {d, Divisors[GCD[n, k]]}]];
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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