Challenge: OSPF neighbor changing state from DOWN to DOWN

I’ve had an interesting discussion with Nicolas who optimized my OSPF neighbor loss EEM applet assuming the OSPF-5-ADJCHG message reports only OSPF neighbor state transitions from DOWN to FULL and from FULL to DOWN. I knew I'd seen stranger messages in my lab and was able to produce these ones after fumbling with OSPF configurations of two routers connected with a serial link:

*19:34:42.765: %OSPF-5-ADJCHG: Process 1, Nbr 10.0.1.1 on Serial1/0 from →
  EXSTART to DOWN, Neighbor Down: Too many retransmissions
*19:35:42.773: %OSPF-5-ADJCHG: Process 1, Nbr 10.0.1.1 on Serial1/0 from →
  DOWN to DOWN, Neighbor Down: Ignore timer expired

The messages are repeated approximately every three minutes (using the default OSPF timers).

Here's the challenge: what was going on and how was I able to produce these messages?