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

0,6

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]

Links

Table of n, a(n) for n=0..45.

Formula

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

Prog

(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

Crossrefs

Column 2 of A284826.

Cf. A056463.

Sequence in context: A268821 A014841 A056476 * A366276 A269386 A252756

Adjacent sequences: A056478 A056479 A056480 * A056482 A056483 A056484

Keyword

nonn

Author

Marks R. Nester

Extensions

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

Status

approved