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A196448 Value of a variable (d) in an iterative system. See equations. 0


%S 0,1,2,48,10240,738197504,3026418949592973312,

%T 57156803818751382534863703592054816768,

%U 19223296064788821505866276808082953452203024798006734264363075470063703162880

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

%C 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.

%C 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

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

%F a' = 2ad + bd;

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

%F c' = be + 2 ce;

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

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

%e 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}.

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

%K nonn

%O 0,3

%A _Daniel Tisdale_, Oct 02 2011

%E a(5)-a(8) from _Franklin T. Adams-Watters_, Oct 03 2011

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)