#Symbolic approach (using transfter matrix)
Help:=proc(): print(` Ising1(z,w,t)`): end:

#Ising1(z,w,t): The generating function, in t, for 
# add(gPF(1,n,z,w)*t^n,t=1..infinity)
#weight enumerator of ALL vectors in {-1,1} with weight
#z^(sum of products of neighbors)*w^(sum of entries)*t^(lenght)
#(of length>=1)
Ising1:=proc(z,w,t) local f,g,var,eq:
#f (g) : weight-enumerator of vectors that start with 1 (-1)

eq:={f=w*t+t*w*z*f+ t*w*z^(-1)*g,
g=w^(-1)*t+ t*w^(-1)*z^(-1)*f+ t*w^(-1)*z*g}:

var:={f,g}:

var:=solve(eq,var):

normal(subs(var,f)+subs(var,g)):

end: