I believe your partitions are fairly messed up. You seem to have lost your Recovery partition and your have 2 Core Storage partitions on physical disk1.
You will have to boot to Internet Recovery to enter these next 2 commands. The purpose of executing these commands is to create a partition so subsequent diskutil commands will not fail. These commands does not recreate the missing Recover partition. You still will not have a Recovery partition.
gpt -f add -b 3518304760 -s 262144 -i 3 -t 426F6F74-0000-11AA-AA11-00306543ECAC /dev/disk1
The next command will format the newly created partition.
newfs_hfs -J -v "Boot OS X" disk1s3
You can now boot back to macOS and enter the next 2 commands.
diskutil cs resizePV 283F0C97-1406-4410-9E1B-7B46DF89373B 0
diskutil cs resizeLV 1F16BBE1-0369-44F2-BDCF-A21CFA0909CC 0
I do not know of a way to replace the missing Recovery partition, other than reinstall macOS. At some point during an upgrade, I image the Recovery partition will be recreated in place of the empty disk1s3.
For now, you can use Internet Recovery, if necessary. Another option would be to download, but not install, High Sierra from the Apps Store. You then could create an USB flash drive installer. This installer would include all of the functionality of the missing Recovery partition. The instructions for creating the flash drive are given at the Apple website: How to create a bootable installer for macOS. Again this is optional, since you can use Internet Recovery.
diskutil cs list. Also, what version of macOS are you using? What is the model/year of your Mac? – David Anderson Feb 24 '18 at 21:14