Journal of Integer Sequences, Vol. 3 (2000), Article 00.2.2

Some Easily Derivable Integer Sequences

Valery A. Liskovets
Institute of Mathematics
National Academy of Sciences, Surganov str. 11
220072, Minsk, BELARUS
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Abstract: We propose and discuss several simple ways of obtaining new enumerative sequences from existing ones. For instance, the number of graphs considered up to the action of an involutory transformation is expressible as the semi-sum of the total number of such graphs and the number of graphs invariant under the involution. Another, less familiar idea concerns even- and odd-edged graphs: the difference between their numbers often proves to be a very simple quantity (such as n!). More than 30 new sequences will be constructed by these methods.

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(Concerned with sequences A000016 A000088 A000171 A000273 A000568 A000595 A000666 A000717 A000831 A001174 A001187 A001349 A001437 A002499 A002500 A002785 A003027 A003030 A003085 A003086 A005176 A005177 A005639 A006125 A006384 A006385 A006799 A006800 A006849 A007080 A007147 A007769 A007869 A018191 A029849 A035512 A049287 A049297 A049309 A053763 A054499 A054913 A054914 A054915 A054930 A054931 A054932 A054933 A054934 A054935 A054936 A054937 A054938 A054939 A054940 A054941 A054942 A054943 A054944 A054945 A054946 A054947 A054948 A054949 A054950 A054951 A054952 A054953 A054954 A054956 A054957 A054958 A054959 A054960 A059735 A059736)

Received Dec. 30, 1999, revised version received May 24, 2000, published in Journal of Integer Sequences Feb. 9, 2001.

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