login
A340458
Minimum length of the string over the alphabet of 3 or more symbols that has exactly n substring palindromes. Substrings are counted as distinct if they start at different offsets.
1
1, 2, 2, 3, 4, 3, 4, 5, 5, 4, 5, 6, 6, 7, 5, 6, 7, 7, 8, 8, 6, 7, 8, 8, 9, 9, 9, 7, 8, 9, 9, 10, 10, 10, 11, 8, 9, 10, 10, 11, 11, 11, 12, 12, 9, 10, 11, 11, 12, 12, 12, 13, 13, 14, 10, 11, 12, 12, 13, 13, 13, 14, 14, 15, 14, 11, 12, 13, 13, 14, 14, 14, 15, 15, 16, 15, 16, 12, 13, 14, 14, 15, 15, 15, 16, 16, 17, 16, 17, 17
OFFSET
1,2
COMMENTS
The uploaded Python script uses G. Manacher's algorithm to efficiently calculate the number of palindromes.
FORMULA
a(k*(k+1)/2) = k, from a string of k identical symbols.
EXAMPLE
The string AAA with length 3 has 6 palindromic substrings:
A starting at offset 1,
A starting at offset 2,
A starting at offset 3,
AA starting at offset 1,
AA starting at offset 2,
AAA starting at offset 1.
There is no shorter string with exactly 6 substring palindromes. So a(6) = 3.
CROSSREFS
Sequence in context: A112342 A256094 A063712 * A185977 A204006 A369879
KEYWORD
nonn
AUTHOR
Serguei Zolotov, Feb 13 2021
STATUS
approved