%I M1748 #19 Jun 15 2022 13:10:28

%S 1,2,7,18,52,133,330,762,1681

%N Number of distinct vertex-degree sequences of n-faced polyhedral graphs.

%D M. B. Dillencourt, personal communication.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Steve Dutch, <a href="https://stevedutch.net/symmetry/polynum0.htm">Enumeration of polyhedra</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Skeleton.html">Skeleton</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Heptahedron">Heptahedron</a>

%e From _Andrey Zabolotskiy_, Jun 15 2022: (Start)

%e All A000944(6) = 7 topologically distinct hexahedra have distinct vertex-degree sequences, so a(6) = 7.

%e There are A000944(7) = 34 heptahedra (polyhedral graphs with 7 faces), but some of them have identical vertex-degree sequences. See Wikipedia for these a(7) = 18 vertex-degree sequences (or, equivalently by polyhedron duality, sets of faces). (End)

%Y Cf. A000944.

%K nonn,more

%O 4,2

%A _N. J. A. Sloane_

%E Name edited by _Michel Marcus_ and _Andrey Zabolotskiy_, Jun 15 2022