A056481 Number of primitive (aperiodic) palindromic structures using exactly two different symbols.

0, 0, 0, 1, 1, 3, 2, 7, 6, 14, 12, 31, 27, 63, 56, 123, 120, 255, 238, 511, 495, 1015, 992, 2047, 2010, 4092, 4032, 8176, 8127, 16383, 16242, 32767, 32640, 65503, 65280, 131061, 130788, 262143, 261632, 524223, 523770, 1048575, 1047494, 2097151, 2096127, 4194162

Offset: 0

Author

Marks R. Nester

Keywords

• nonn

Comments

Permuting the symbols will not change the structure. Identical to A056476 for n>1.

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]

Crossrefs

Column 2 of A284826.

Cf. A056463.

Programs

Python

from sympy import mobius, divisors
def A056481(n): return sum(mobius(n//d)<<(d-1>>1) for d in divisors(n, generator=True)) if n>1 else 0 # Chai Wah Wu, Feb 18 2024

Formula

a(n) = A056476(n) - A000007(n) - A000007(n-1).

Extensions

More terms (using A056476) from Joerg Arndt, May 22 2021