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A114943 as a simple table

na(n)
23
342
4333
543431
6444234
74343434
844442113
94434333131
1043433423421
11444342132443
124444434444114
13444344434443444
144444444244242143
1544444344444311111
16444444442312244142
1744444343333321221114

[3,42,333,43431,444234,4343434,44442113,
 4434333131,43433423421,444342132443,4444434444114,
 444344434443444,4444444244242143,
 44444344444311111,444444442312244142,
 44444343333321221114]