A056515 Number of primitive (period n) periodic palindromic structures using a maximum of four different symbols.

1, 1, 1, 1, 3, 4, 10, 14, 35, 49, 127, 186, 463, 714, 1799, 2789, 6996, 11050, 27685, 43946, 109925, 175259, 438495, 700074, 1750445, 2798246, 6996927, 11188856, 27973533, 44747434, 111873782, 178973354, 447438656, 715860463, 1789673215, 2863377048, 7158463662

Offset: 0

Author

Marks R. Nester

Keywords

• nonn

Comments

For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome. Permuting the symbols will not change the structure.

References

• M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A056478, A056505, A285037.

Formula

a(n) = Sum_{d|n} mu(d)*A056505(n/d) for n > 0.

Moebius transform of A056505.

a(n) = Sum_{k=1..4} A285037(n, k) for n > 0. - Andrew Howroyd, Oct 01 2019

Extensions

a(0)=1 prepended and terms a(17) and beyond from Andrew Howroyd, Oct 01 2019