A306473 a(n) is the maximum number of distinct palindromic not necessarily contiguous subwords over all binary words of length n.

1, 2, 3, 5, 7, 10, 14, 18, 25, 32, 43, 54, 72, 90, 119, 148, 195, 242, 318, 394

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

Conjectures from Colin Barker, Feb 18 2019: (Start)

G.f.: x*(1 + x + x^3 + x^6 - x^7 + x^8) / ((1 - x)*(1 - x^2 - x^4)).

a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) for n>9.

(End)

Example

The word 0110 has the distinct palindromes (0, 010, 0110, 1, 11) and no other 4-length word has more, so a(4)=5.

Crossrefs

Sequence in context: A130053 A177277 A025488 * A175846 A088585 A304712

Adjacent sequences: A306470 A306471 A306472 * A306474 A306475 A306476

Keyword

nonn,base,more

Author

Lars Blomberg, Feb 18 2019

Status

approved