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Amtrak is running a special offer where if you take the Acela on a Saturday between March 14 and June 13, 2015, you can save an additional 25%. Unfortunately this is on for NYC to Washington, D.C. (and vice versa). While this is a very specific route, if you need to hop the train during this time it could definitely save you some money.
Even though you can travel through mid-June, you must book by April 30 and at least 14 days prior to your desired date. You can learn more about this offer here.