The table entries are developed only through three levels of growth, corresponding to the depth in Figure 4. The prefixed e is included in the set names to indicate that the envisioned root is a member of the extended set of parents of left descents. An sss sequence not rooted in the e set will be a set (16n+15) containing 4 times the number of elements as the anchored set developed here for the esss sequence (64n+15). Each dn+c formula denotes the set of odd integers congruent to c mod d.
Allowed Applied Resulting Terminating
From Subset Move Transform Result Set Name Set Names
e 24n+5 s (2(24n+5)-1)/3 16n+3 es
24n+13 b (4(24n+13)-1)/3 32n+17 eb
24n+21 null et
es 48n+3 null est
48n+19 b (4(48n+19)-1)/3 64n+25 esb
48n+35 s (2(48n+35)-1)/3 32n+23 ess
eb 96n+17 s (2(96n+17)-1)/3 64n+11 ebs
96n+49 b (4(96n+49)-1)/3 128n+65 ebb
96n+81 null ebt
esb 192n+25 b (4(192n+25)-1)/3 768n+33 esbb
192n+89 s (2(192n+89)-1)/3 384n+59 esbs
192n+153 null esbt
ess 96n+23 s (2(96n+23)-1)/3 64n+15 esss
96n+55 b (4(96n+55)-1)/3 128n+73 essb
96n+87 null esst
ebs 192n+11 s (2(192n+11)-1)/3 128n+7 ebss
192n+75 null ebst
192n+139 b (4(192n+139)-1)/3 256n+185 ebsb
ebb 384n+65 s (2(384n+65)-1)/3 256n+43 ebbs
384n+193 b (4(384n+193)-1)/3 512n+257 ebbb
384n+321 null ebbt
Figure 5: Stepwise Development of Abstract Generation Tree Rooted in Extended Parents , Showing Set Contents