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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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COMMENTS
| T(h,k)=number of periodic binary words of k 1's and h-k 0's.
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EXAMPLE
| 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
| A050186 := proc(n, k)
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:
A050870 := proc(n, k)
binomial(n, k)-A050186(n, k) ;
end proc:
seq(seq(A050870(n, k), k=0..n), n=0..20) ; # R. J. Mathar, Sep 24 2011
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CROSSREFS
| Cf. A007318. Different from A053200.
Sequence in context: A025426 A204246 A053200 * A103306 A163510 A124735
Adjacent sequences: A050867 A050868 A050869 * A050871 A050872 A050873
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 29 2008
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