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

1,1

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.

Links

Table of n, a(n) for n=1..9.

Example

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.

Sequence in context: A340738 A368593 A218684 * A337614 A343908 A100408

Adjacent sequences: A379997 A379998 A379999 * A380007 A380014 A380015

Keyword

nonn,more,new

Author

Pontus von Brömssen, Jan 09 2025

Status

approved