Barry Williams Hopes to 'Carry the Torch' for “Brady Bunch” Mom Florence Henderson on “DWTS” (Exclusive)

The '70s icon — who's competing on 'Dancing with the Stars' 13 years after Henderson became the then-oldest competitor ever — also tells PEOPLE which of his TV siblings he's invited to the ballroom

Barry Williams is following in the footsteps of his Brady Bunch TV mom Florence Henderson.

Late last month, Williams began his journey competing on Dancing with the Stars alongside partner Peta Murgatroyd. His arrival on the popular ABC competition series comes 13 years after Henderson — who died in November 2016 at age 82 — competed on the show's 11th season in 2010.

Making his debut in the Dancing with Stars ballroom, Williams, 69, and Murgatroyd, 37, even performed a foxtrot to "It's a Sunshine Day" by The Brady Bunch.

Williams, who played Greg Brady on the beloved series, tells PEOPLE he "thought it was a perfect number" as he looks back on the other Brady Bunch stars who've appeared on the show before him.

Related: 'Brady Bunch' Star Susan Olsen Looks Back on Romance Chatter About Florence Henderson and Barry Williams

"The Brady Bunch and Dancing with the Stars have alumni. Florence Henderson was here in 2010, Maureen McCormick in 2016. Each went several weeks," he recalls. "So, there is a  kind of a family atmosphere, the difference being that no Brady has taken it all the way to the end. So  I'm hopeful that I'm going to be that person."

Williams also reveals Henderson, who played his onscreen mom Carol Brady, previously suggested he try to get invited onto Dancing with the Stars.

"I try and channel Florence Henderson, who encouraged me to pursue an invitation for Dancing With the Stars," he shares. "Being familiar with my theatrical background, she felt that I could do very well. And at that time, she had just been eliminated and asked if I would carry the torch."

The Brady Bunch cast has remained close in the years since it concluded in 1974 after five seasons. Because of that, Williams believes some of his former costars will soon hit the ballroom to cheer him on as he competes for the newly renamed Len Goodman Mirrorball Trophy.

Related: The 'Brady Bunch' Cast: Where Are They Now?

"They've all been invited, so we'll see," he says. "I have Christopher Knight on my guest list for next week. He and I do a podcast called The Real Brady Bros, which is an episodic recap. We each watch an episode and then dissect it on our podcast and the details, what we were thinking, what our perspectives are now, et cetera. But it's very Brady and he's very supportive and that brings us into contact on a very regular basis."

Williams adds, "Maureen has reached out several times, cheering me on, and hopefully, she will come. Hopefully, they'll all come. Susan Olsen has already reached out for a date, but it's not specified yet. ... I have a lot of Brady support."

Besides Williams, Henderson, McCormick (Marcia Brady), Knight (Peter Brady) and Olsen (Cindy Brady), the series also starred Robert Reed (Mike Brady), Eve Plumb (Jan Brady), Mike Lookinland (Bobby Brady) and Ann B. Davis (Alice).

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Dancing with the Stars airs Tuesdays at 8 p.m. ET on ABC and Disney+.

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