This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380000 #5 Jan 09 2025 08:43:00
%S A380000 2,7,18,163,1454,21837,492116,23699853,1507394232
%N A380000 Number of sequences over {0,1,...,n-1} containing no two consecutive blocks with the same average.
%C A380000 See A379914 for details.
%C A380000 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.
%e A380000 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.
%Y A380000 Row sums of A379998.
%Y A380000 Cf. A379914, A379999.
%K A380000 nonn,more
%O A380000 1,1
%A A380000 _Pontus von Brömssen_, Jan 09 2025