A196448 Value of a variable (d) in an iterative system. See equations.

0, 1, 2, 48, 10240, 738197504, 3026418949592973312, 57156803818751382534863703592054816768, 19223296064788821505866276808082953452203024798006734264363075470063703162880

Offset

0,3

Comments

In genetics, one could ask, given an initial population of genotypes xX and XY (x being a recessive sex-linked trait), how many afflicted males would result in successive generations if each generation mated only inter sese, and each pairing resulted in only the expected four hypothetical results.

In any system of this kind, provided the sex ratio is 1:1, the frequency of each allele is the same in each subsequent generation, and the genome ratios approach the product values fairly quickly. (If the sex ratios are not equal in the base generation, they will be from the first generation on.) In this case, this results in a limit of 1/3 of males affected, and 1/9 of females. - Franklin T. Adams-Watters, Oct 02 2011

Links

Table of n, a(n) for n=0..8.

Formula

a = xx, b = xX, c = XX, d = xY, e = XY.

a' = 2ad + bd;

b' = 2ae + bd + be + 2cd;

c' = be + 2 ce;

d' = bd + be + 2ad + 2ae;

e' = bd + be + 2cd + 2ce.

Example

Let F_0 be: a=0,b=1,c=0,d=0,e=1; F_1 is {0,1,1,1,1}; F_2 = {1,4,3,2,6}.

Crossrefs

Cf. A196197, A058891 (males in each generation), A000302 (total size of generations).

Sequence in context: A053071 A238838 A002820 * A053290 A056989 A352207

Adjacent sequences: A196445 A196446 A196447 * A196449 A196450 A196451

Keyword

nonn

Author

Daniel Tisdale, Oct 02 2011

Extensions

a(5)-a(8) from Franklin T. Adams-Watters, Oct 03 2011

Status

approved