A379999 - 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

%O 1,2

%A _Pontus von Brömssen_, Jan 09 2025