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A056498 Number of primitive (period n) periodic palindromes using exactly two different symbols. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)