A056481 - OEIS

%I #25 Feb 19 2024 01:48:47

%S 0,0,0,1,1,3,2,7,6,14,12,31,27,63,56,123,120,255,238,511,495,1015,992,

%T 2047,2010,4092,4032,8176,8127,16383,16242,32767,32640,65503,65280,

%U 131061,130788,262143,261632,524223,523770,1048575,1047494,2097151,2096127,4194162

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

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

%D 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]

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

%o (Python)

%o from sympy import mobius, divisors

%o 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

%Y Column 2 of A284826.

%Y Cf. A056463.

%K nonn

%O 0,6

%A _Marks R. Nester_

%E More terms (using A056476) from _Joerg Arndt_, May 22 2021