What are these character sequences in connection with DTMF and a modem (telephony)?
The long defunct Hayes corporation's proprietary "AT" command set.

The DLE (ASCII Data Link Escape) character is used for reporting of received DTMF (i.e. non-control and non-data signals) by V22(etc) modems. 

I guess the repetition is associated with the 95 ms default duration for DTMF tone generated by the ATDT command in Hayes modems. If the user holds the key down for longer than 95mS, multiple DLE "4" sequences are reported. This potentially allows the receiving equipment to distinguish long and short presses.

See Wikipedia

Standardization (the lack of)

Note that all this originated as a proprietary single-manufacturer "standard" which has been extended by other manufacturers without oversight by any standards body. You should expect poor documentation and inconsistency. 

There may be some limited standardization in specific fields of use as the Hayes AT command set crept into other realms (e.g. GSM) but I doubt there's a single body overseeing the standardization of everything associated with AT commands in all fields of technology.

Conclusion

For precise information you'd have to obtain information from the producer of the specific modem device (or chipset). Any other source of documentation is potentially misleading.