A family of restricted subadditive recursions (Q1850124)

A system of certain restricted subadditive recursions \(U_k\) is solved and several closed form expression for \(U_{2p}\) with \(p\) being a fixed non-negative integer is duly exibited. In an earlier work the author proved that \(U_{2p}\) also satisfies a certain periodic system of \(p+1\) difference equation. In this paper the author determines a sufficient condition for \(U_{2p+1}\) to satisfy a single (solvable) difference equation. It transpires that this finding on \(U_{2p+1}\) is a special case of a general conclusion on members of a certain family of restricted subadditive recursion.