Exact next nearest neighbor degeneracy Available to Purchase

It is shown that A [n₁₁, n₁₀₁, n₁₁₁, q, N], the arrangement degeneracy arising when q indistinguishable particles are placed on a one‐dimensional lattice of N equivalent compartments so that n₁₁ occupied nearest neighbors, n₁₀₁ next nearest neighbors of the 101‐type, and n₁₁₁ next nearest neighbors of the 111‐type are created, is given by $A[n11, n101, n111, q, N]=(N−2q+n11+2q−n11−n101)(q−n11−1n101)(q−n11n11−n111)(n11−1n111)$⁠. The normalization and first moment of the next nearest neighbor density are determined. Similar results for the vacant next nearest neighbor degeneracy are also presented.