Various Sequences from Counting 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.

arXiv comment6 pages. Changes: 1) Include references to the sequences after Table 1; 2) Correct a miscalculation in Table 1 discovered by N. J. A. Sloane; 3) Add a remark at the end to mention the recurrence found by A. Heinz