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

0,5

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)*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

Crossrefs

Cf. A056478, A056505, A285037.

Sequence in context: A106523 A007068 A121720 * A056516 A056517 A285042

Adjacent sequences: A056512 A056513 A056514 * A056516 A056517 A056518

Keyword

nonn

Author

Marks R. Nester

Extensions

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

Status

approved