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math.CO2012★ 3 cited
Nested recursions with ceiling function solutions
Abraham Isgur, Vitaly Kuznetsov, Stephen M. Tanny
Consider a nested, non-homogeneous recursion R(n) defined by R(n) = \sum_{i=1}^k R(n-s_i-\sum_{j=1}^{p_i} R(n-a_ij)) + nu, with c initial conditions R(1) = xi_1 > 0,R(2)=xi_2 > 0,…
math.CO2012★ 1 cited
A combinatorial approach for solving certain nested recursions with non-slow solutions
Abraham Isgur, Vitaly Kuznetsov, Stephen Tanny
We define the generalized Golomb triangular recursion by g_{j,s,lambda}(n) = g_{j,s,lambda}(n - s - g_{j,s,lambda}(n-j)) + λj. For particular choices of the initial conditions, we…