A144841 a(n) = 280*C(n,9)+10*C(n,6)+6*C(n,4)+C(n,3)+1 where C = binomial.

1, 1, 2, 11, 41, 121, 316, 757, 1961, 6281, 22166, 74031, 221937, 596961, 1460096, 3294761, 6945521, 13818417, 26161386, 47446611, 82880281, 140069161, 229877572, 367512861, 573882201, 877268601, 1315379326, 1937825527, 2809097761, 4012108241, 5652377096, 7862946641, 10810114657, 14700084961, 19786641106

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

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

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.

Crossrefs

Cf. A000127.

Programs

Magma

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

Formula

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

Extensions

More terms and new name using formula given from Joerg Arndt, Aug 21 2025