Voozh

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

(list; graph; refs; listen; history; text; internal format)

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