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A296604
Number of Johnson solids with n faces.
6
0, 0, 0, 0, 1, 2, 1, 4, 2, 4, 3, 4, 2, 8, 1, 3, 3, 4, 0, 6, 1, 4, 0, 2, 0, 4, 3, 0, 0, 1, 0, 5, 0, 1, 0, 0, 3, 0, 0, 0, 0, 7, 0, 0, 0, 0, 1, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0
OFFSET
1,6
COMMENTS
Sum(n>0, a(n)) = 92, the number of Johnson solids, as conjectured by Johnson and proved by Zalgaller.
a(n) > 0 if and only if n is a member of A296603.
LINKS
Norman W. Johnson, Convex Polyhedra with Regular Faces, Canadian Journal of Mathematics, 18 (1966), 169-200.
Eric Weisstein's World of Mathematics, Johnson Solid.
Victor A. Zalgaller, Convex Polyhedra with Regular Faces, Zap. Nauchn. Sem. LOMI, 1967, Volume 2. Pages 5-221 (Mi znsl1408).
FORMULA
a(62) = 5.
a(n) = 0 for n > 62.
EXAMPLE
The square pyramid is the only Johnson solid with five faces, so a(5) = 1.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Jan 28 2018
STATUS
approved