A new equivalent-neighbour model is introduced in which the spins within a hypercube of volume (2R+1)d interact equally with the spin at the centre of the hypercube. The lattice dimensionality d and the range of the interaction R are variables. The concept of the coincidable occurrence factors is introduced. Connections between the coincidable occurrence factors and the high-temperature lattice constants are shown. A systematic way of deriving the high-temperature lattice constants through the use of the coincidable occurrence factors is developed. The high-temperature lattice constants are derived up to eighth order. The extension of d and R from integers to real values is discussed. The present model can also be extended to an anisotropic one in which the ranges of interactions are different in different lattice directions.