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%I A006869 M1748 #19 Jun 15 2022 13:10:28
%S A006869 1,2,7,18,52,133,330,762,1681
%N A006869 Number of distinct vertex-degree sequences of n-faced polyhedral graphs.
%D A006869 M. B. Dillencourt, personal communication.
%D A006869 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006869 Steve Dutch, <a href="https://stevedutch.net/symmetry/polynum0.htm">Enumeration of polyhedra</a>
%H A006869 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Skeleton.html">Skeleton</a>
%H A006869 Wikipedia, <a href="https://en.wikipedia.org/wiki/Heptahedron">Heptahedron</a>
%e A006869 From _Andrey Zabolotskiy_, Jun 15 2022: (Start)
%e A006869 All A000944(6) = 7 topologically distinct hexahedra have distinct vertex-degree sequences, so a(6) = 7.
%e A006869 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 A006869 Cf. A000944.
%K A006869 nonn,more
%O A006869 4,2
%A A006869 _N. J. A. Sloane_
%E A006869 Name edited by _Michel Marcus_ and _Andrey Zabolotskiy_, Jun 15 2022

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