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a(n) is the number of different types of faces of Johnson solid J_n, with solids ordered by indices in Johnson's paper.
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%I #16 Mar 13 2021 11:06:22

%S 2,2,3,3,4,3,2,2,3,2,2,1,1,2,2,2,1,3,3,4,4,3,3,4,3,2,2,2,2,3,3,3,3,2,

%T 2,2,2,3,3,3,3,3,3,2,2,3,3,2,2,2,1,3,3,3,3,3,3,2,2,2,2,2,2,2,3,3,3,4,

%U 4,4,4,3,3,3,3,4,4,4,4,4,4,4,4,1,2,2,2,2,2,2,3,4

%N a(n) is the number of different types of faces of Johnson solid J_n, with solids ordered by indices in Johnson's paper.

%C A299529(x) equals the number of times the value x occurs as a term in this sequence. In particular, if A299529(x) = 0, then x does not occur in this sequence.

%D V. A. Zalgaller, Convex Polyhedra with Regular Faces, in: Seminars in mathematics, Springer, 1969, ISBN 978-1-4899-5671-2.

%H N. W. Johnson, <a href="https://doi.org/10.4153/CJM-1966-021-8">Convex Polyhedra with Regular Faces</a>, Canadian Journal of Mathematics 18 (1966), 169-200.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/List_of_Johnson_solids">List of Johnson solids</a>

%H V. A. Zalgaller, <a href="http://mi.mathnet.ru/eng/znsl1408">Convex Polyhedra with Regular Faces</a>, Zapiski Nauchnykh Seminarov LOMI 2 (1967), 5-221.

%e For n = 5: Johnson solid J_5 is the pentagonal cupola. This solid is bounded by 5 equilateral triangles, 5 squares, 1 pentagon and 1 decagon. Thus, there are 4 types of polygons making up the faces of this solid, hence a(5) = 4.

%Y Cf. A242731, A242732, A242733, A296603, A296604, A299529.

%K nonn,fini,full

%O 1,1

%A _Felix Fröhlich_, Mar 17 2019

%E a(68) corrected and a(88)-a(92) added by _Pontus von Brömssen_, Mar 13 2021