Greensky Bluegrass — led by singer Paul Hoffman, left — can play more genres than the band’s name implies. (Jamie VanBuhler)

Greensky Bluegrass, which formed in Michigan in 2000, didn’t play its first gig in D.C. until September 2013, when it sold out The Hamilton. Returning a few months later, the band moved up to the larger 9:30 Club and earned another sellout. In January 2015, Greensky doubled up at the V Street nightclub and sold out both nights. This weekend, the group goes for a three-peat with a trio of shows at the famed venue.

“We’ve never not sold out a show in D.C.,” singer and mandolin player Paul Hoffman says. “We’ve been shocked by all of it — flattered, really.”

It’s the same kind of success the band has found across the country — especially at music festivals, where Greensky has moved from bottom of the bill to, in some case, headliner status.

“We’ve been clicking all along but for the first five years it was a real slow click,” Hoffman says. “Then we got to a place where we started earning better exposure at festivals and more people saw us. We were a rehearsed band by that point so people liked it, and it’s all steamrolled into one big thing.”

One secret to the group’s success has been its dedication to making every show special. That means putting in work before playing a note. The quintet changes the setlist each night and improvises, so for a three-night run in one city, the group has to come up with three unique shows, each split into two sets of music.

“It’s intense,” Hoffman says. “It’s a very difficult math equation. We make a map before we start and split songs up that need to be separated.”

They’ll consider what they’ve already played that week, what they played the last time they were in town and what they haven’t played in the while.

“The shows have different vibes because of the way we write stuff, so one will have a more psychedelic vibe, and one will have a more aggressive, rock ’n’ roll vibe and one will have a more song vibe,” Hoffman says. “We try to make them all even, but it never really works that way.”

Despite the band’s name — and the fact that its members play acoustic guitar, mandolin, banjo, upright bass and dobro — Greensky Bluegrass isn’t strictly a bluegrass band. Depending on the song, the group can do rock, folk, reggae, funk — even heavy metal. The group’s most recent album, 2014’s “If Sorrows Swim,” is more folk rock than traditional bluegrass.

“I think it’s something we’ll battle forever,” Hoffman says of the name. “We’ve discussed whether we should just be Greensky and take Bluegrass out to eliminate that preconceived notion but the wordplay doesn’t make any sense without both words. Ultimately, being a word guy, I’m willing to disprove people.”

One way the band does that is through its eclectic mix of covers. Last time Greensky played 9:30 Club, the group covered songs by Prince, Talking Heads, Jerry Garcia, Traveling Wilburys, Bob Marley, Traffic, Phish, the Beatles, Van Morrison and George Clinton — some of which were given bluegrass makeovers. Fans can expect an equally diverse batch of covers this time around.

“We overthink the s— out of it,” Hoffman says of the setlists. “But the most important thing is, that means we care about it, and I think that’s what translates to the crowd.”

9:30 Club, 815 V St. NW, Thu., 7 p.m., $23, Fri. & Sat., 7 p.m., sold out.

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