

A299529


Number of Johnson solids with exactly n types of faces.


4



5, 35, 35, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET

1,1


COMMENTS

The possible types of faces of a Johnson solid are triangles, squares, pentagons, hexagons, octagons, and decagons. See A299114 comments.


LINKS

Table of n, a(n) for n=1..84.
Norman W. Johnson, Convex Polyhedra with Regular Faces, Canadian Journal of Mathematics, 18 (1966), 169200.
Eric W. Weisstein, MathWorld: Johnson Solid
Wikipedia, List of Johnson solids
Victor A. Zalgaller, Convex Polyhedra with Regular Faces, Zap. Nauchn. Sem. LOMI, 1967, Volume 2. Pages 5221 (Mi znsl1408).


FORMULA

Sum(n>0, a(n)) = 92, the number of Johnson solids.
a(n) = 0 for n>4.


EXAMPLE

Each of the five Johnson solids J12, J13, J17, J51, J84 has only one type of face, so a(1) = 5.


CROSSREFS

Cf. A299114, A299530.
Sequence in context: A199584 A087675 A128044 * A014632 A117985 A115707
Adjacent sequences: A299526 A299527 A299528 * A299530 A299531 A299532


KEYWORD

nonn


AUTHOR

Jonathan Sondow, Feb 11 2018


STATUS

approved



