Seq A235647 gives for each n the number of loops ("chains", "acts of replacement") that arrive as the result of investigating, which steps of conflict consolidation are necessary to resolve the place - amount contradictions implicated by a change in order concepts.

A235647 connects A000027 and A000217. For each n of A000027 there are A000217 records generated in a database. The generation of the records is driven by two loops, the outside, called “a”, counting 1 to n; the inside loop, called “b”, counts from a to n. Each element of the collection of values (a,b) receives a sequential number, called sqab (presently appears identical to A000027), and concurrently one b*(b-1)/2+a. This sequence, called sqba, will appear in the form of the sequence A000027 to the human spectator, if, after production, the collection is sequentially reordered by a procedure called sorting, namely on first b, second a. A235647 shows, how many “chains” of sequential, pairwise conflicts arise, as the transformation between sqab and sqba takes place. If the elements are in sequential order sqba, then sqba appears in the form of A000027 and sqab appears as a permutation of A000027. Both sqab and sqba can appear once as A000027, and once not, in dependence of the elements’ sequential order in the database. The task is to consolidate the first A000217 elements of A000027 into a specific permutation, which is generated by two loops of A000027, second, b, nested in the first, a.

The SET ORDER TO <arg> command brings forth differing sequences of the records if <arg> is “b,a” to that if <arg> is “a,b”.

The conflict can be approached two ways: 1) on place i, in sequential order sqab element (a1,b1) stands, while in sequential order sqba, on place i stands element (a2,b2) while (a1,b1) {=|≠} (a2,b2); 2) element (a,b) stands in sequential order sqab on place i, but in sequential order sqba on place j while i {=|≠} j.

The conflict resolution between sqab and sqba is done by acts of replacements. An act of replacement will involve 1 or more elements. If sqab[i] = sqba[i], the act of replacement contains 1 element. This is also called a chain of length 1. If sqab[i] ≠ sqba[i] but sqba[j], then sqab[j] may or may not refer to sqab[i] (the start value). If it does, the chain has length 2, the act of replacement has involved two elements, that have changed places directly. (Please see in Examples case for A27=3) The chain continues until such a k that sqba[k]=sqab[i], then the chain is closed. (Please see in Examples case for A27=4) How many steps were necessary to reach sqba[k]=sqab[i] for each chain during the reorder from the state of the collection in sequential order sqab into the state of the collection in the sequential order sqba, is not recorded in A235647; it gives the aggregate number of acts of replacements, chains, as a(n). A235647 gives also the number of summands of a specific partition, constructed by these rules, on A000217.