Number of Ancestors in a Given Generation Back

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

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