OFFSET
1,2
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Scott R. Shannon, Colored illustration for n = 2
Scott R. Shannon, Illustration for n=3 showing interior vertices color-coded according to multiplicity.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
Theorem: a(n) = n*(17*n^3-30*n^2+19*n-4)/2.
From Colin Barker, May 27 2020: (Start)
G.f.: x*(1 + 45*x + 123*x^2 + 35*x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
EXAMPLE
Scott Shannon's illustration for n=2 shows 29 interior intersection points, of which 20 are simple intersections, 8 are triple intersections, and one (the central point) is a 4-fold intersection. A point where d lines meet is equivalent to C(d,2) simple points. So a(2) = 20*1 + 8*3 + 1*6 = 50.
PROG
(PARI) Vec(x*(1 + 45*x + 123*x^2 + 35*x^3) / (1 - x)^5 + O(x^30)) \\ Colin Barker, May 31 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Scott R. Shannon and N. J. A. Sloane, May 18 2020
STATUS
approved