Here's what a google search turned up. Does this resemble what you were talking about? I've never seen these at Japanese restaurants before (but then, there's only 1 in town where I live, but they serve a great bean-sprout salad as a starter).....
"Title: Japanese-Style Carrot Sticks
1 c rice vinegar; (not seasoned)
1/3 c sugar
1/2 ts salt
1 lb carrots; cut into sticks
In a saucepan cook vinegar, sugar, and salt over moderately high heat,
stirring occasionally, until sugar is dissolved and mixture is hot. Put
carrots in a heatproof ceramic or glass dish and pour vinegar mixture over
them. Marinate carrots, covered and shilled, at least 4 hours and up to 1
Makes about 4 cups.
Gourmet May 1996"