A056498 Number of primitive (period n) periodic palindromes using exactly two different symbols.

0, 1, 2, 3, 6, 7, 14, 18, 28, 39, 62, 81, 126, 175, 246, 360, 510, 728, 1022, 1485, 2030, 3007, 4094, 6030, 8184, 12159, 16352, 24381, 32766, 48849, 65534, 97920, 131006, 196095, 262122, 392364, 524286, 785407, 1048446, 1571310, 2097150, 3143497, 4194302, 6288381

Offset: 1

Author

Marks R. Nester

Keywords

• nonn

Comments

For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome.

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 = 1..1000

Crossrefs

Column 2 of A327878.

Cf. A027383, A056463.

Programs

PARI

seq(n)={Vec(sum(k=1, n\2, moebius(k)*x^(2*k)*(1 + x^k)/((1 - x^k)*(1 - 2*x^(2*k))) + O(x*x^n)), -n)} \\ Andrew Howroyd, Sep 29 2019

Formula

a(n) = Sum_{d|n} mu(d)*A027383(n/d-2) assuming that A027383(-1)=0.

G.f.: Sum_{k>=1} mu(k)*x^(2*k)*(1 + x^k)/((1 - x^k)*(1 - 2*x^(2*k))). - Andrew Howroyd, Sep 29 2019

Extensions

Terms a(32) and beyond from Andrew Howroyd, Sep 28 2019