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A144841
Conjectured values for maximal number of regions obtained by joining each triple of n points on a 3 dimensional sphere by a plane.
0
1, 1, 2, 11, 41, 121, 316, 757, 1961, 6281, 22166, 74031, 221937, 596961, 1460096, 3294761, 6945521, 13818417, 26161386, 47446611
OFFSET
1,3
COMMENTS
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.
FORMULA
a(n) = 280*C(n,9)+10*C(n,6)+6*C(n,4)+C(n,3)+1.
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]
PROG
(Magma) function a(n) return 280*Binomial(n, 9)+10*Binomial(n, 6)+6*Binomial(n, 4)+Binomial(n, 3)+1; end function;
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Sep, Jorik & Noud Thijssen (sep.thijssen(AT)gmail.com), Sep 22 2008
STATUS
approved