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

0,5

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

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

Crossrefs

Cf. A056477, A056504, A285037.

Sequence in context: A244703 A232801 A357238 * A151517 A219043 A342570

Adjacent sequences: A056511 A056512 A056513 * A056515 A056516 A056517

Keyword

nonn

Author

Marks R. Nester

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

Status

approved