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- W1974786255 abstract "For a fixed non-negative integer k, let U k ={ U k ( n )}, n ⩾0, denote that sequence which is defined by the initial conditions U k (0)= U k (1)= U k (2)=⋯= U k ( k )=1, and by the restricted subadditive recursion U k (n+k+1)= min 0⩽l⩽[k/2] (U k (n+l)+U k (n+k−l)), n⩾0. U k is important in the theory of optimal sequential search for simple real zeros of real valued continuous kth derivatives. The structure of U k depends substantially on the parity of k. In an earlier work, the author proved that U 2 p (p a fixed non-negative integer) also satisfies a certain periodic system of p +1 difference equations . This system was solved, and several closed form expressions for U 2 p ( n ), n >2 p , were duly exhibited. In contrast, much less is known about the behaviour of U 2 p +1 , although it has been conjectured that it satisfies, eventually, a single (solvable) difference equation. In this paper, the author determines a sufficient condition for U 2 p +1 to satisfy this equation. It transpires that this finding on U 2 p +1 is a special case of a general conclusion on members of a certain family of restricted subadditive recursions." @default.
- W1974786255 created "2016-06-24" @default.
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- W1974786255 date "2002-12-01" @default.
- W1974786255 modified "2023-10-17" @default.
- W1974786255 title "A family of restricted subadditive recursions" @default.
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- W1974786255 doi "https://doi.org/10.1016/s0166-218x(01)00335-3" @default.
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