%I #5 Sep 08 2022 08:45:38

%S 1,1,2,11,41,121,316,757,1961,6281,22166,74031,221937,596961,1460096,

%T 3294761,6945521,13818417,26161386,47446611

%N Conjectured values for maximal number of regions obtained by joining each triple of n points on a 3 dimensional sphere by a plane.

%C This is the first step in the generalization of the maximal number of regions obtained by joining n points around a circle by straight lines. See A000127.

%F a(n) = 280*C(n,9)+10*C(n,6)+6*C(n,4)+C(n,3)+1.

%F Empirical G.f.: x*(1-9*x+37*x^2-84*x^3+111*x^4-76*x^5+9*x^6+18*x^7+274*x^8-x^9)/(1-x)^10. [Colin Barker, Feb 15 2012]

%o (Magma) function a(n) return 280*Binomial(n,9)+10*Binomial(n,6)+6*Binomial(n,4)+Binomial(n,3)+1; end function;

%Y A000127

%K easy,nonn

%O 1,3

%A Sep, Jorik & Noud Thijssen (sep.thijssen(AT)gmail.com), Sep 22 2008