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.

3, 7, 12, 17, 22, 30, 39, 45, 56, 66, 77, 90

Offset

1,1

Comments

In other words, the contiguous substrings of length n are all different if we interpret them as multisets.

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.

Links

Table of n, a(n) for n=1..12.

Bert Dobbelaere, C++ program

MathOverflow, Sequences with 3 Letters

Example

Maximal strings for n = 1, 2, ..., 8 are:
012
0011220
011122200012
00111122220000121
0100212111000002222211
001011112122220200001012120200
010010220212110100000202222212111110100
021200201101121220202000010111111212222220200

Crossrefs

Sequence in context: A310246 A310247 A350426 * A310248 A298022 A227133

Adjacent sequences: A332260 A332261 A332262 * A332264 A332265 A332266

Keyword

nonn,more,hard

Author

Nathaniel Johnston, Feb 08 2020

Extensions

a(9)-a(12) from Bert Dobbelaere, Feb 09 2020

Status

approved