It is gone.
If you saved the game after you killed it then it is gone forever.
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In Pokemon HeartGold and SoulSilver, you can find Articuno in the Seafoam Island cave. There is a small series of puzzles you have to solve, but eventually you'll get to Articuno which is at level 50
Yes, all 3 of them (Articuno, Zapdos and Moltres) will be in Pokémon HeartGold and Pokémon SoulSilver.
Articuno will disappear once you defeat it in HeartGold however you can bring it back in its place within Seafoam Island by defeating the Elite 4 and Lance regardless of whether you've already defeated them or not. Defeating Lance will activate the regeneration process for any Pokémon such as Articuno that is either considered a Legendary or a one-off Pokémon such as Sudowoodo.
it wil never come back...
It will come and kill you in your sleep. Goodnight