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A143823
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Number of subsets {x(1),x(2),...,x(k)} of {1,2,...,n} such that all differences |x(i)-x(j)| are distinct.
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10
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1, 2, 4, 7, 13, 22, 36, 57, 91, 140, 216, 317, 463, 668, 962, 1359, 1919, 2666, 3694, 5035, 6845, 9188, 12366, 16417, 21787, 28708, 37722, 49083, 63921, 82640, 106722, 136675, 174895, 222558, 283108, 357727, 451575, 567536, 712856, 890405, 1112081, 1382416, 1717540
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| See A143824 for sizes of the largest subsets of {1,2,...,n} with the desired property.
a(n) = A169947(n-1) + n + 1 for n>=2.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..60
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EXAMPLE
| {1,2,4} is a subset of {1,2,3,4}, with distinct differences 2-1=1, 4-1=3, 4-2=2 between pairs of elements, so {1,2,4} is counted as one of the 13 subsets of {1,2,3,4} with the desired property. Only 2^4-13=3 subsets of {1,2,3,4} do not have this property: {1,2,3}, {2,3,4}, {1,2,3,4}.
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MAPLE
| b:= proc(n, s) local sn, m;
if n<1 then 1
else sn:= [s[], n];
m:= nops(sn);
`if` (m*(m-1)/2 = nops (({seq (seq (sn[i]-sn[j],
j=i+1..m), i=1..m-1)})), b(n-1, sn), 0) +b(n-1, s)
fi
end:
a:= proc(n) option remember;
b(n-1, [n]) +`if` (n=0, 0, a(n-1))
end:
seq (a(n), n=0..30); # Alois P. Heinz, Sep 14 2011
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CROSSREFS
| Cf. A143824.
Sequence in context: A061257 A061255 A088111 * A119983 A151897 A192758
Adjacent sequences: A143820 A143821 A143822 * A143824 A143825 A143826
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Sep 02 2008
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EXTENSIONS
| a(21)-a(29) and connection to A169947 from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Nov 12 2010
Corrected a(21)-a(29) and more terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 14 2011
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