In the days after the horrific shooting at Sandy Hook Elementary School, gun enthusiasts rushed to buy millions of firearms, driven by fears that the massacre would spark new gun legislation. Those restrictions never became a reality, but a new study concludes that all the additional guns caused a significant jump in accidental firearm deaths.

The study, published Thursday in the journal Science, estimates that the 3 million guns sold in the several months after Sandy Hook caused about 60 more accidental gun deaths than would have occurred otherwise. Children were killed in a third of them — some 20 youngsters, the same number as died at Sandy Hook.

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“It’s a serious and provocative study, but it’s important to keep in mind that in the grand scheme of things, accidental deaths are relatively rare,” said David M. Studdert, a professor at Stanford Law School. “Suicides and homicides, that’s the main game that researchers are trying to figure out when it comes to the causal relationships between guns and mortality.”