a(n) is the first Zagreb index of the polymer B[n,1], defined pictorially in the Bodroža-Pantić et al. reference (Fig. 4).
a(n) is the first Zagreb index of the polymer B[n,2], defined pictorially in the Bodroža-Pantić et al. reference (Fig. 4).
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
The M-polynomial of B[n,1] is M(B[n,1]; x,y) = 2*(2*n+1)*x^2*y^2 + 4*(n+1)*x^2*y^3 + (13*n-8)*x^3*y^3.
The M-polynomial of B[n,2] is M(B[n,1]; x,y) = 2*(n+2)*x^2*y^2 + 8*n*x^2*y^3 + (11*n-6)*x^3*y^3.