Recurrences & Integer Sequences

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Abstractions about recurrence relations, recursive probability calculations, elimination problems, and named or constant-recursive number sequences.

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Constant-recursive sequence — A sequence satisfying a fixed finite-order linear recurrence with constant coefficients.
• Josephus problem — The recurrence problem of locating the survivor or elimination order when positions in a circle are removed at a fixed counting interval.
• Leonardo number — A recurrence sequence beginning with one and one in which each later term is the sum of the previous two plus one.
• Panjer recursion — A recursive algorithm for computing an aggregate-loss distribution when claim counts belong to the Panjer (a,b,0) class and severities are discrete or discretized.
• Recurrence relation — An equation defining terms of a sequence from earlier terms together with enough initial conditions to select a solution.