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

1,3

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

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

Prog

(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

Crossrefs

Column 2 of A327878.

Cf. A027383, A056463.

Sequence in context: A319811 A000837 A200144 * A325093 A018652 A125686

Adjacent sequences: A056495 A056496 A056497 * A056499 A056500 A056501

Keyword

nonn

Author

Marks R. Nester

Extensions

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

Status

approved