Various Sequences from Counting Subsets

TL;DR

This paper investigates the enumeration of subsets of the set {1, 2, ..., n} under various conditions and analyzes the resulting sequences as n grows.

Contribution

It introduces new counting sequences for subsets with specific properties and explores their behavior as n increases.

Findings

Derived explicit formulas for subset counts under different conditions.

Identified growth patterns and recurrence relations of the sequences.

Provided insights into the combinatorial structures of constrained subsets.

Abstract

We count the number of subsets of $\{1,2,\cdots,n\}$ under different conditions and study the sequence obtained as we let $n$ increase.