Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #19 Dec 19 2016 01:41:32
%S 3,9,24,51,102,177,294,459,690,987,1380,1875,2508,3279,4212,5319,6648,
%T 8199,10026,12141,14580,17343,20496,24051,28068,32547,37542,43071,
%U 49218,55983,63456,71661,80658,90447,101100,112635,125160,138675,153252,168915,185784
%N Number of distinct lines passing through at least two points in a triangular grid of side n.
%H Heinrich Ludwig, <a href="/A244504/b244504.txt">Table of n, a(n) for n = 2..1000</a>
%F 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_.
%t 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_ *)
%o (PARI) g(j) = if (j > 0, j*(j+1)/2, 0);
%o a(n) = 3*sum(j = 1, n-1, eulerphi(j)*(g(n-j)-g(n-2*j))); \\ _Michel Marcus_, Sep 04 2014
%Y Cf. A234248.
%K nonn
%O 2,1
%A _Heinrich Ludwig_, Sep 04 2014