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TableĀ 1 Number of generated alkane isomers by canonical augmentation algorithm and isomer transformation algorithm

From: Molecular structures enumeration and virtual screening in the chemical space with RetroPath2.0

No. of carbon atoms No. of structures output by canonical augmentation algorithm No. of structures output by isomer transformation algorithm No. of iterations for isomer transformation algorithm
1 1 1 1
2 2 1 1
3 3 1 1
4 5 2 2
5 8 3 3
6 13 5 3
7 22 9 4
8 40 18 5
9 75 35 5
10 150 75 6
11 309 159 7
12 664 355 7
13 1466 802 8
14 3324 1858 9
15 7671 4347 9
16 18,030 10,359 10
17 42,924 24,894 10
18 103,447 60,523 10
  1. The numbers agree with earlier calculations [30]. For a given number of carbon atoms (N), the canonical augmentation generates all alkanes from 1 to N carbon atoms, while the isomer transformation enumeration generates alkanes having only N carbon atoms, one can thus verify that at any given number of carbon atoms N, the numbers of structures generated by the canonical augmentation algorithm equals the sum of numbers of isomers generated by the transformation algorithm up to N