These rules may be iterated to, e.g., combine n doublets (s =1/2) to obtain the Clebsch-Gordan decomposition series, (Catalan's triangle), 2 ⊗ ⊗ n = ⨁ ⨁ k = 0 ⌊ ⌊ n / 2 ⌋ ⌋ ( n + 1 − − 2 k n + 1 ( n + 1 k ) ) ( n + 1 − − 2 k ) , where ⌊ ⌊ n / 2 ⌋ ⌋ is the integer floor function ; and the number preceding the boldface irreducible representation dimensionality (2 j +1) label indicates multiplicity of that representation in the representation reduction. For instance, from this formula, addition of three spin 1/2s yields a spin 3/2 and two spin 1/2s, 2 ⊗ ⊗ 2 ⊗ ⊗ 2 = 4 ⊕ ⊕ 2 ⊕ ⊕ 2 .