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%I #17 Jan 26 2024 15:55:47
%S 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,
%T 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
%N Number of Johnson solids with n faces.
%C Sum(n>0, a(n)) = 92, the number of Johnson solids, as conjectured by Johnson and proved by Zalgaller.
%C a(n) > 0 if and only if n is a member of A296603.
%H Norman W. Johnson, <a href="http://dx.doi.org/10.4153/CJM-1966-021-8">Convex Polyhedra with Regular Faces</a>, Canadian Journal of Mathematics, 18 (1966), 169-200.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JohnsonSolid.html">Johnson Solid</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/List_of_Johnson_solids">List of Johnson solids</a>.
%H Victor A. Zalgaller, <a href="http://mi.mathnet.ru/eng/znsl1408">Convex Polyhedra with Regular Faces</a>, Zap. Nauchn. Sem. LOMI, 1967, Volume 2. Pages 5-221 (Mi znsl1408).
%F a(62) = 5.
%F a(n) = 0 for n > 62.
%e The square pyramid is the only Johnson solid with five faces, so a(5) = 1.
%Y Cf. A181708, A242731, A296602, A296603.
%K nonn
%O 1,6
%A _Jonathan Sondow_, Jan 28 2018
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