A334893 Number of subsets of [n] avoiding 3-term arithmetic progressions and containing n if n>0.

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

Offset: 0

Author

Alois P. Heinz, May 14 2020

Keywords

• nonn

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..80
• Eric Weisstein's World of Mathematics, Nonaveraging Sequence
• Wikipedia, Arithmetic progression
• Wikipedia, Salem-Spencer set
• Index entries related to non-averaging sequences

Crossrefs

Row sums of A334892.

Partial sums give A051013.

Programs

Maple

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);

Mathematica

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}];
a /@ Range[0, 23] (* Jean-François Alcover, May 03 2021, after Alois P. Heinz *)