The Padovan sequence uses the same skip-one recurrence as Perrin, \(P(n) = P(n-2) + P(n-3)\), but from seeds 1, 1, 1: it runs 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49.
Geometrically it is the spiral-of-triangles counterpart to the Fibonacci spiral of squares: equilateral triangles with Padovan side lengths wind into a spiral. Like Perrin, its growth rate is the plastic number ≈ 1.3247. Named for architect Richard Padovan, who attributed the proportional system to Dom Hans van der Laan; popularized by Ian Stewart's Scientific American column.