A241220 - OEIS

%I #12 Sep 19 2017 03:42:38

%S 0,15,84,312,852,1878,3654,6546,10680,16668,25002,35910,50136,68190,

%T 90462,118200,152274,192828,240480,296880,361962,437832,525756,625440,

%U 739146,867864,1011822,1174062,1354572,1554114,1775568,2020848,2289054,2582760,2905410

%N Number of lines through at least two points of a centered hexagonal grid of size n.

%C A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice.

%H Andrew Howroyd, <a href="/A241220/b241220.txt">Table of n, a(n) for n = 1..200</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HexNumber.html">Hex Number</a>.

%o (PARI)

%o c(n,s,fmin,fmax)={sum(k=1+s, n, max(0, fmax(k-s)-max(fmin(k)-1,if(k-2*s>0,fmax(k-2*s)))))}

%o b(n, u, v)={c(2*n-1, u, i->max(0,i-n)+1+i\u*v, i->min(i,n)+n-1+i\u*v)}

%o a(n)={3*((n>1)*(2*n-1) + sum(u=1, 2*n-3, sum(v=1, 2*n-2-u, if(gcd(u,v)==1, b(n,u,v), 0))))} \\ _Andrew Howroyd_, Sep 18 2017

%Y Cf. A018808, A241219, A003215.

%K nonn

%O 1,2

%A _Martin Renner_, Apr 17 2014

%E a(15)-a(16) from _Martin Renner_, Apr 27 2014

%E Terms a(17) and beyond from _Andrew Howroyd_, Sep 18 2017