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Diana, Goddess of the Hunt for Ancestors!
 
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Number of Ancestors in a Given Generation
 
The formula for the number of ancestors in a given generation is:
2n = x
where n is the number of generations back
and x equals the number of individuals in that generation.
Based on the table below, if you go back 40 generations, you have over two trillion ancestors!  Of course, this number doesn't mean you have that many unique ancestors in 40 generations.  What is happening is repetition of ancestors, that is, the same ancestors appearing over and over again in a pedigree.  Repetition seldom appears within the first ten generations, but the further back you go, the more repetition you are likely to find.

As an example of repetition of ancestors, there is a famous pedigree that begins having significant repetition within the first few generations:  that of outlaw, Jesse JAMES.  There is even more pronounced repetition in his wife's pedigree, so the repetition is further compounded for their children:

Pedigrees of Jesse Woodson JAMES & Zerelda Cole MIMS

When repetition happens in the near generations, we call it "inbreeding."  It happens so often among southerners, like Jesse & Zerelda, that it's become a cultural cliché, as in the movie,  Deliverance.

The table below is based on an average generation time of 30 years and uses a person born in 1950 as an example.

 
GENERATIONS BACK NUMBER OF INDIVIDUALS BIRTH
Each Generation (x) Cumulative
Name of Generation n Decimal Binary Decimal Year
self 0 1 1 1 1950
parents 1 2 2 3 1920
grandparents 2 4 4 7 1890
great-grandparents 3 8 8 15 1860
2nd great-grandparents 4 16 16 31 1830
3rd great-grandparents 5 32 32 63 1800
4th great-grandparents 6 64 64 127 1770
5th great-grandparents 7 128 128 255 1740
6th great-grandparents 8 256 256 511 1710
7th great-grandparents 9 512 512 1023 1680
8th great-grandparents 10 1024 1K 2047 1650
9th great-grandparents 11 2048 2K 4095 1620
10th great-grandparents 12 4096 4K 8191 1590
11th great-grandparents 13 8192 8K 16,383 1560
12th great-grandparents 14 16,384 16K 32,767 1530
13th great-grandparents 15 32,768 32K 65,535 1500
14th great-grandparents 16 65,536 64K 131,071 1470
15th great-grandparents 17 131,072 128K 262,143 1440
16th great-grandparents 18 262,144 256K 524,287 1410
17th great-grandparents 19 524,288 512K 1,048,575 1380
18th great-grandparents 20 1,048,576 1M 2,097,151 1350
19th great-grandparents 21 2,097,152 2M 4,194,303 1320
20th great-grandparents 22 4,194,304 4M 8,388,607 1290
21st great-grandparents 23 8,388,608 8M 16,777,215 1260
22nd great-grandparents 24 16,777,216 16M 33,554,431 1230
23rd great-grandparents 25 33,554,432 32M 67,108,863 1200
24th great-grandparents 26 67,108,864 64M 134,217,727 1170
25th great-grandparents 27 134,217,728 128M 268,435,455 1140
26th great-grandparents 28 268,435,456 256M 536,870,911 1110
27th great-grandparents 29 536,870,912 512M 1,073,741,823 1080
28th great-grandparents 30 1,073,741,824 1G 2,147,483,647 1050
29th great-grandparents 31 2,147,483,648 2G 4,294,967,295 1020
30th great-grandparents 32 4,294,967,296 4G 8,589,934,591  990
31st great-grandparents 33 8,589,934,592 8G 17,179,869,183  960
32nd great-grandparents 34 17,179,869,184 16G 34,359,738,367  930
33rd great-grandparents 35 34,359,738,368 32G 68,719,476,735  900
34th great-grandparents 36 68,719,476,736 64G 137,438,953,471  870
35th great-grandparents 37 137,438,953,472 128G 274,877,906,943  840
36th great-grandparents 38 274,877,906,944 256G 549,755,813,887  810
37th great-grandparents 39 549,755,813,888 512G 1,099,511,627,775  780
38th great-grandparents 40 1,099,511,627,776 1T 2,199,023,255,551  750

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