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A334893
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Number of subsets of [n] avoiding 3-term arithmetic progressions and containing n if n>0.
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3
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1, 1, 2, 3, 6, 10, 17, 25, 41, 63, 109, 165, 262, 412, 643, 932, 1459, 2163, 3212, 4601, 6817, 9904, 14741, 20906, 30352, 43993, 63540, 89442, 132037, 187587, 266842, 378061, 535907, 751709, 1077809, 1499972, 2084027, 2951390, 4114165, 5651914, 7968177
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OFFSET
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0,3
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LINKS
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MAPLE
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b:= proc(n, s) option remember; `if`(n<1, 1, b(n-1, s)+
`if`(ormap(j-> 2*j-n in s, s), 0, b(n-1, s union {n})))
end:
a:= n-> b(n-1, {n}):
seq(a(n), n=0..23);
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MATHEMATICA
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b[n_, s_] := b[n, s] = If[n < 1, 1, b[n-1, s] +
If[AnyTrue[s, MemberQ[s, 2 # - n]&], 0, b[n-1, s ~Union~ {n}]]];
a[n_] := b[n-1, {n}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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