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We have exhaustively enumerated all simple, connected graphs of a finite order and have computed a selection of invariants over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia of Integer Sequences (OEIS). 141 new sequences were added and six sequences were extended. From the graph database, we were able to programmatically suggest relationships among the invariants. It will be shown that we can readily visualize any sequence of graphs with a given criteria. The code has been released as an open-source framework for further analysis and the database was constructed to be extensible to invariants not considered in this work. [ABSTRACT FROM AUTHOR]

Text The sequence of middle divisors is shown to be unbounded. For a given number n , a n , 0 is the number of divisors of n between n / 2 and 2 n . We explicitly construct a sequence of numbers n ( i ) and a list of divisors in the interesting range, so that the length of the list goes to infinity as i increases. Video For a video summary of this paper, please visit https://youtu.be/drODtRj0gjM . [ABSTRACT FROM AUTHOR]

Abstract: In this study, we compute the spectral norm of the matrix , where are ith components of any integer sequence . Also, we give a corollary and examples related to spectral norm. [Copyright &y& Elsevier]

In this brief note, we formulate some modifications of the Pell-Jacobsthal numbers, which belong to a more general class, the Lucas sequences. [ABSTRACT FROM AUTHOR]