Sly Stone, the influential, eccentric and preternaturally rhythmic singer, songwriter, multi-instrumentalist and producer whose run of hits in the late 1960s and early ’70s with his band the Family Stone could be dance anthems, political documents or both, died on Monday at home in the Granada Hills neighborhood of Los Angeles. He was 82. The cause was “a prolonged battle with C.O.P.D.,” or chronic obstructive pulmonary disease, “and other underlying health issues,” his representatives said in a statement. As the colorful maestro and mastermind of a multiracial, mixed-gender band, Mr. Stone experimented with the R&B, soul and gospel music he…