A 555 can drive most relays directly.
Here are some bits and pieces that might do what you want. Now I know what was left out--IC ID. Start with 555-OSC, A; 555-OS, one shot, B; 555-FF, flip-flop, C; 555-INV-R, D; up E; F; 4017- G; OR-H; INV-I.
No telling at what state everything will be in at power-up, but cycling thru once should make avery thing normal?
First SW push puts out a .1 to 1 s + pulse to cover up any SW bounce. resets C which is already reset,& advances 4017- G, one count. THe first stage of G, 0, pin-3 is high at reset so " 1' is used as first active step. When G-2, goes hi D-3 goes lo turning on R LED. Secsnd push turns on G LED, 3rd B LED. 4th push puts a hi on I input, output lo sets FF C. C-3 goes hi , enabling OSC, A. G continuously recycles, resetting every time G-1 goes hi. If SW is pushed again, FF, C is reset, stopping the clock - at a random output. May want to add an OR to G reset and diffrentiate C out for a secondary reset pulse. Wanted to keep first cut simple. Would prob. use a NOR IC for the OR & INV.
A review might be helpfull??

thanks for the schematic, after a real quick look through ( I am currently doing my sons school stuff and took a second to check my thread) I think I understand some of whats going on,, I think I can definitely build this, I like the explanation but its gonna take a lot questions for me to truly understand whats really happening even though I can build it.. make any sense to you?? I can read a schematic well enough to be dangerous and can build circuits that work from them even though I don't understand whats going on.. anyway,, Im not sure why I burnt so many 555's out trying to drive a relay then,, I got the relays from an old tv set and don't have any data on them, after just looking at them they are spst, NO, 12v 20a relays... even thought I had a 12v PSU the voltage to the 555 was stepped down to 5v in a multivibrator config and I was trying to use it to trigger the relay to switch the output back up to 12v.. I ended up building a transistor scr tha completelty replace the 555 circuit altogether.. That was my first project in electronics and is what sparked my interest into building circuits and started the learning journey im now on..lol

 

On relay, at 12V rating & 80Ωs or higher coil resistance should work, but relay needs a snubber- a diode asross the coil, cathode to +V supply; I also like to use a diode in series, anode to pin 3.

 

Added two ICs , 4001 NOR, 4009 NOT [ invertor], to add a reset to G on 5th push of SW. Notice strange location of gnd. on I. Combination of H & I gives a OR, so that G receives a clock pulse from either SW or A.
Question-- why the over use of the " Quote" ?

 

thanks for the schematic.. and I use the " " when I think the term im using is not the appropriate term and by putting it in quotes it lets the readers know im aware of it,lol, and it usually gets a response of the right term. Im trying to learn everything from scratch here and I think Im doing a fairly decent job of it. I use () and " " a lot and I tend to ramble a bit when im either confused or unsure. Also, It seems that when I don't use them or over explain myself, somebody always mentions that im using the wrong term or not being thorough enough..lol.. but alas, Im sorry if I make it harder to understand me by doing this. I do believe that I'm getting better at communicating with the electronics gurus here at aac. thanks for the criticism... I always try to make it constructive..

 

No critisim intended, just an old mans irritation of the over use of the quote key by all users of AAC. It is usefull if the subject is several posts back so that an answer corisponds to the question.