Let Σ = {0, 1} be the binary alphabet, and A = {0, 01, 11} be the set of three strings 0, 01, 11 over Σ. Let A^* denote the Kleene closure of A, ⁰ the set of nonnegative integers, and ⁺ the set of positive integers. A sequence in A^* is called a Jacobsthal binary sequence. Let J(n) denote the set of Jacobsthal binary sequences of length n. For k ∊ ⁺, {s₁, s₂, . . . , s_k} ⊂ ⁰, and n − 1 ≥ s₁ > s₂ > .. . > s_k ≥ 0, let J₁(n; s₁, s₂, . . . , s_k) denote the subset J₁(n; s₁, s₂, . . . , s_k) = {a_n−1a_n−2 . . . a₁a₀ ∊ J(n) : a_si = 1 (1 ≤ i ≤ k)}, of J(n), and let N₁(n; s₁, s₂, . . . , s_k) = |J₁(n; s₁, s₂, . . . , s_k)|. When k = 1, a formula for N₁(n; s) has been derived recently. In this paper we consider the general case of N₁(n; s₁, s₂, . . . , s_k), and study some other special types of Jacobsthal binary sequences. Some identities involving these numbers are also given.