A non-decreasing sequence of positive integers is (Î±, Î²)-Conolly, or Conollylike for short, if for every positive integer m the number of times that m occurs in the sequence is Î± + Î²rm, where rm is 1â€¦ (More)

For k > 1 and nonnegative integer parameters ap, bp, p = 1..k, we analyze the solutions to the meta-Fibonacci recursion C(n) = âˆ‘k p=1 C(n âˆ’ ap âˆ’ C(n âˆ’ bp)), where the parameters ap, bp, p = 1..kâ€¦ (More)

We study the recursions A(n) = A(nâˆ’aâˆ’A(nâˆ’b))+A(A(nâˆ’b)) where a â‰¥ 0, b â‰¥ 1 are integers and the superscript k denotes a k-fold composition, and also the recursion C(n) = C(n âˆ’ s âˆ’ C(n âˆ’ 1)) + C(n âˆ’ sâ€¦ (More)

We define the generalized Golomb triangular recursion by gj,s,Î»(n) = gj,s,Î»(nâˆ’ sâˆ’gj,s,Î»(nâˆ’j))+Î»j. For particular choices of the initial conditions, we show that the solution of the recursion is aâ€¦ (More)

It is known that, for given integers s â‰¥ 0 and j > 0, the nested recursion R(n) = R(n âˆ’ s âˆ’ R(n âˆ’ j)) + R(n âˆ’ 2j âˆ’ s âˆ’ R(n âˆ’ 3j)) has a closed form solution for which a combinatorial interpretationâ€¦ (More)

We apply a tree-based methodology to solve new, very broadly defined families of nested recursions of the general form R(n) = âˆ‘k t=1R(nâˆ’ at âˆ’ âˆ‘p i=1R(nâˆ’ bti)), where at are integers, bti are naturalâ€¦ (More)