Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Jan 09 2025 09:08:00
%S 1,2,8,6,38,2,12,8,2
%N Number of longest sequences over {0,1,...,n-1} containing no two consecutive blocks with the same average.
%C a(n) is the last element of row n in A379998.
%C The sequences counted by a(n) have length A379914(n).
%C a(n) is even for all n >= 2, because each term x in a sequence can be replaced by n-1-x, giving another sequence of maximum length.
%e For 1 <= n <= 4, the following sequences are counted:
%e n | longest sequences
%e --+-----------------------------------------------------
%e 1 | 0
%e 2 | 010, 101
%e 3 | 010, 012, 020, 101, 121, 202, 210, 212
%e 4 | 0203202, 1310131, 1310313, 2023020, 2023202, 3130131
%Y Cf. A379914, A379998, A380000.
%K nonn,more,new
%O 1,2
%A _Pontus von Brömssen_, Jan 09 2025