A365538 a(0) = 1; otherwise, for i >= 0, a(4i+0) = a(4i+1) = a(2i), a(4i+2) = 2*a(2i+1), a(4i+3) = 0.

1, 1, 2, 0, 2, 2, 0, 0, 2, 2, 4, 0, 0, 0, 0, 0, 2, 2, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 4, 4, 0, 0, 4, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Roland Kneer, Oct 23 2023

Keywords

• nonn
• tabf
• easy

Comments

Related to a model of X-chromosome inheritance:

The two X chromosomes of a female are inherited one from each parent, while the X chromosome of a male is always inherited from his mother. Thus, the probability distribution of inheritance from the parents (mother, father) is (0.5, 0.5) for a female and (1, 0) for a male. For the inheritance of any X-chromosome of a female from the 2^i ancestors of the i-th generation before (right to left on an ahnentafel), the distribution is given by the first 2^i terms of the sequence, divided by 2^i. For example, the X-chromosome of a man, which was inherited from his mother, was inherited from his mother's 16 great-great-grandparents with probabilities 1/16, 1/16, 1/8, 0, 1/8, 1/8, 0, 0, 1/8, 1/8, 1/4, 0, 0, 0, 0, 0.

Links

• Roland Kneer, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A280873, A003754.

Positions of 0's: A004780 (complement of A003714).

Formula

This sequence regarded as a triangle with rows of lengths 1, 1, 2, 4, 8, 16, ...:

1;

1;

2, 0;

2, 2, 0, 0;

2, 2, 4, 0, 0, 0, 0, 0;

2, 2, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;

...