A380000 Number of sequences over {0,1,...,n-1} containing no two consecutive blocks with the same average.

2, 7, 18, 163, 1454, 21837, 492116, 23699853, 1507394232

Offset: 1

Author

Pontus von Brömssen, Jan 09 2025

Keywords

• nonn
• more

Comments

See A379914 for details.

a(n) is even if and only if n is odd; for each sequence can be paired up with its complement (where all terms x are replaced by n-1-x), and the only self-complementary sequences (that also satisfy the consecutive blocks condition) are the empty sequence and those with a single term (n-1)/2 for odd n.

Examples

			For n = 3, the a(3) = 18 sequences are: (), 0, 1, 2, 01, 02, 10, 12, 20, 21, 010, 012, 020, 101, 121, 202, 210, 212.
		

Crossrefs

Row sums of A379998.

Cf. A379914, A379999.