A056514 Number of primitive (period n) periodic palindromic structures using a maximum of three different symbols.

1, 1, 1, 1, 3, 4, 9, 13, 28, 39, 84, 121, 244, 364, 741, 1088, 2200, 3280, 6591, 9841, 19720, 29510, 59169, 88573, 177240, 265716, 531804, 797121, 1594684, 2391484, 4783968, 7174453, 14350000, 21523238, 43050000, 64570064, 129143196, 193710244, 387430329, 581130368, 1162271280

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. A056477, A056504, A285037.

Formula

a(n) = Sum_{d|n} mu(d)*A056504(n/d) for n > 0.

Moebius transform of A056504.

a(n) = Sum_{k=1..3} A285037(n, k) for n > 0. - Andrew Howroyd, Apr 08 2017

Extensions

Corrected by Franklin T. Adams-Watters and T. D. Noe, Oct 25 2006

a(17)-a(35) from Andrew Howroyd, Apr 08 2017

a(0)=1 prepended and terms a(36) and beyond from Andrew Howroyd, Oct 01 2019