A334894 Number of maximal subsets of [n] avoiding 3-term arithmetic progressions and containing n if n>0.

1, 1, 1, 2, 2, 1, 3, 6, 15, 4, 20, 7, 18, 6, 1, 3, 10, 29, 54, 123, 2, 16, 44, 170, 2, 31, 2, 10, 24, 70, 1, 10, 2, 2, 10, 26, 2, 2, 82, 221, 20, 1, 3, 10, 27, 58, 167, 408, 831, 2005, 4216, 14, 36, 106, 2, 6, 18, 30, 2, 2, 2, 8, 34, 2, 2, 4, 8, 12, 80, 211

Offset: 0

Author

Alois P. Heinz, May 14 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..136
• Eric Weisstein's World of Mathematics, Nonaveraging Sequence
• Wikipedia, Arithmetic progression
• Wikipedia, Iverson bracket
• Wikipedia, Salem-Spencer set
• Index entries related to non-averaging sequences

Crossrefs

Last elements of rows of A334892.

Cf. A003002, A262347, A334187.

Formula

a(n) = A262347(n) - [n > 0 and A003002(n) = A003002(n-1)] * A262347(n-1).

a(n) = A334892(n,A003002(n)).

a(n) = A334187(n,A003002(n)) - [n > 0] * A334187(n-1,A003002(n)).