A144841 Conjectured values for maximal number of regions obtained by joining each triple of n points on a 3 dimensional sphere by a plane.

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.

Links

Table of n, a(n) for n=1..20.

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

A000127

Sequence in context: A173580 A062256 A024522 * A203245 A121244 A203574

Adjacent sequences: A144838 A144839 A144840 * A144842 A144843 A144844

Keyword

easy,nonn

Author

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

Status

approved