A056463 Number of primitive (aperiodic) palindromes using exactly two different symbols.

0, 0, 2, 2, 6, 4, 14, 12, 28, 24, 62, 54, 126, 112, 246, 240, 510, 476, 1022, 990, 2030, 1984, 4094, 4020, 8184, 8064, 16352, 16254, 32766, 32484, 65534, 65280, 131006, 130560, 262122, 261576, 524286, 523264, 1048446, 1047540, 2097150, 2094988, 4194302, 4192254

Offset

1,3

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)*A056453(n/d).

G.f.: Sum_{k>=1} mu(k)*2*x^(3*k)/((1 - 2*x^(2*k))*(1 - x^k)). - Andrew Howroyd, Sep 29 2019

Prog

(PARI) seq(n)={Vec(sum(k=1, n\3, moebius(k)*2*x^(3*k)/((1 - 2*x^(2*k))*(1 - x^k)) + O(x*x^n)), -n)} \\ Andrew Howroyd, Sep 29 2019
(Python)
from sympy import mobius, divisors
def A056463(n): return sum(mobius(n//d)*((1<<(d+1>>1))-2) for d in divisors(n, generator=True)) # Chai Wah Wu, Feb 18 2024

Crossrefs

Column 2 of A327873.

Cf. A056453, A056458.

Sequence in context: A321451 A285943 A100495 * A309694 A325263 A365380

Adjacent sequences: A056460 A056461 A056462 * A056464 A056465 A056466

Keyword

nonn

Author

Marks R. Nester

Extensions

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

Status

approved