A244504 Number of distinct lines passing through at least two points in a triangular grid of side n.

3, 9, 24, 51, 102, 177, 294, 459, 690, 987, 1380, 1875, 2508, 3279, 4212, 5319, 6648, 8199, 10026, 12141, 14580, 17343, 20496, 24051, 28068, 32547, 37542, 43071, 49218, 55983, 63456, 71661, 80658, 90447, 101100, 112635, 125160, 138675, 153252, 168915, 185784

Offset: 2

Author

Heinrich Ludwig, Sep 04 2014

Keywords

• nonn

Links

• Heinrich Ludwig, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A234248.

Programs

Mathematica

g[i_]:=If[i>0,i*(i+1)/2,0]; Table[3*Sum[EulerPhi[j]*(g[n-j]-g[n-2*j]),{j,1,n-1}],{n,2,50}] (* Vaclav Kotesovec, Sep 04 2014 after Jon E. Schoenfield *)

PARI

g(j) = if (j > 0, j*(j+1)/2, 0);
a(n) = 3*sum(j = 1, n-1, eulerphi(j)*(g(n-j)-g(n-2*j))); \\ Michel Marcus, Sep 04 2014

Formula

a(n) = 3*sum(j = 1..n-1, euler_phi(j)*(g(n-j)-g(n-2*j))), where g(i) = i*(i+1)/2 if i > 0, otherwise 0, after Jon E. Schoenfield.