A196197 -id:A196197 - cp's OEIS frontend

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

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

Offset: 0

Daniel Tisdale, Oct 02 2011

nonn

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

			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}.

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

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.

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

cp's OEIS Frontend

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

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