A306473 - OEIS

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

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OFFSET

1,2

LINKS

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

KEYWORD

nonn,base,more

AUTHOR

STATUS

approved