A056516 Number of primitive (period n) periodic palindromic structures using a maximum of five different symbols.

1, 1, 1, 1, 3, 4, 10, 14, 36, 50, 137, 201, 548, 854, 2417, 3839, 11060, 18001, 52599, 86471, 254982, 421989, 1252695, 2079474, 6196990, 10306747, 30795387, 51263890, 153409228, 255514354, 765389950, 1275163904, 3821990040, 6368612099, 19095299549, 31821472593

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. A056479, A056506, A285037.

Formula

a(n) = Sum_{d|n} mu(d)*A056506(n/d) for n > 0.

Moebius transform of A056506. - T. D. Noe, Oct 25 2006

a(n) = Sum_{k=1..5} A285037(n, k) for n > 0. - Andrew Howroyd, Oct 01 2019

Extensions

Corrected by T. D. Noe, Oct 25 2006

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