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A332263 Maximal length of a string over the alphabet {0,1,2} with the property that its contiguous substrings of length n all have different quantities of 0's, 1's, or 2's.

%I A332263 #14 Feb 09 2020 10:41:21
%S A332263 3,7,12,17,22,30,39,45,56,66,77,90
%N A332263 Maximal length of a string over the alphabet {0,1,2} with the property that its contiguous substrings of length n all have different quantities of 0's, 1's, or 2's.
%C A332263 In other words, the contiguous substrings of length n are all different if we interpret them as multisets.
%C A332263 Since there are binomial(n+2,2) different triples of nonnegative integers summing up to n, we have the bound a(n) <= binomial(n+2,2)+n-1. Equality holds if and only if n <= 3.
%H A332263 Bert Dobbelaere, <a href="/A332263/a332263.cpp.txt">C++ program</a>
%H A332263 MathOverflow, <a href="https://mathoverflow.net/questions/268428/sequences-with-3-letters">Sequences with 3 Letters</a>
%e A332263 Maximal strings for n = 1, 2, ..., 8 are:
%e A332263 012
%e A332263 0011220
%e A332263 011122200012
%e A332263 00111122220000121
%e A332263 0100212111000002222211
%e A332263 001011112122220200001012120200
%e A332263 010010220212110100000202222212111110100
%e A332263 021200201101121220202000010111111212222220200
%K A332263 nonn,more,hard
%O A332263 1,1
%A A332263 _Nathaniel Johnston_, Feb 08 2020
%E A332263 a(9)-a(12) from _Bert Dobbelaere_, Feb 09 2020